tag:blogger.com,1999:blog-17325237619238058912024-03-14T11:41:55.088-07:00Plano, línea, puntoPlano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-1732523761923805891.post-91284872398131464832016-06-11T08:57:00.001-07:002016-06-11T10:21:53.798-07:00EJERCICIOS RESUELTOS ABATIMIENTOS Y DESABATIMIENTOS
Ejercicio de abatimiento de un punto respecto al plano horizontal:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/R2pMUZ3u/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de un punto respecto al plano vertical:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/j2uF7W2h/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de una recta cualquiera respecto al plano horizontal:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/UvVzEdKZ/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de una recta cualquiera respecto al plano vertical:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/RDneXurZ/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio abatimiento de una recta horizontal respecto al plano horizontal:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/CFkytmrN/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio abatimiento de una recta frontal respecto al plano vertical:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/k8SJbudm/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de la traza vertical de un plano:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/X49uXHJb/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de la traza horizontal de un plano:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/nePbYpH6/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de una figura plana:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/MycpX68j/width/750/height/500/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="500px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de la traza vertical de un plano abierto:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/y7ny7ZTW/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de abatimiento de una figura plana 02:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/qyZW8Ywh/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio de verdadera magnitud de un ángulo entre dos rectas:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/wBHXFdUT/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Abatimiento de una figura plana contenida en un plano de canto:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/aqQ89Gdw/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio abatimiento de la recta t respecto al plano vertical:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/vUNPPqmE/width/750/height/500/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="500px" style="border:0px;"> </iframe>
Ejercicio abatimiento de la recta s respecto al plano vertical:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/fasCspBp/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio desabatimiento de la traza de un plano:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/wUGsmg4C/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio desabatimiento de una figura plana:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/w7BNApdq/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio desabatimiento de un cuadrado:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/CP3D6drx/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Ejercicio desabatimiento de un pentágono:
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/tV7PXGtk/width/750/height/550/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="750px" height="550px" style="border:0px;"> </iframe>
Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-63299901378017083882016-05-20T11:28:00.000-07:002016-05-20T11:34:07.873-07:00GEOMETRÍA DESCRITIVA _ SISTEMA LIBRE<!--[if !mso]>
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<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-insideh-themecolor: background1; mso-border-insideh-themeshade: 217; mso-border-insideh: .5pt solid #D9D9D9; mso-border-insidev-themecolor: background1; mso-border-insidev-themeshade: 217; mso-border-insidev: .5pt solid #D9D9D9; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-table-layout-alt: fixed; mso-yfti-tbllook: 1184; width: 100%px;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td colspan="5" style="background: #0070C0; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="color: white; mso-ansi-language: ES; mso-themecolor: background1;">GEOMETRÍA
DESCRIPTIVA _ SISTEMA LIBRE</span></b><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES;"></span></b></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">La <b style="mso-bidi-font-weight: normal;">geometría descriptiva</b> es el conjunto de técnicas de carácter
geométrico que permite representar el espacio tridimensional sobre una
superficie bidimensional. Dos de estas técnicas son el sistema diédrico y el
sistema libre.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">El denominado <b style="mso-bidi-font-weight: normal;">“Sistema Libre”</b> es más flexible que
el tradicional sistema diédrico, dando relevancia a las líneas de referencia
y orientando el modelo hacia una geometría espacial más conceptual; el modelo
se basa en entender la aplicación de las relaciones pitagóricas y proyectivas
elementales.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Para obtener la
representación de los diferentes elementos en el sistema libre, sólo es
necesaria la dirección de los planos de proyección, y no su posición concreta
en el espacio.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">De la misma manera, en cuanto
tenemos dos o más puntos, el sistema se independiza de la línea de tierra. </span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td colspan="5" style="background: #0070C0; border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="color: white; mso-ansi-language: ES; mso-themecolor: background1;">PROYECCIÓN
DE LA RECTA EN EL SISTEMA DIÉDRICO Y EN EL SISTEMA LIBRE + VERDADERAS MAGNITUDES</span></b><span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Para entender mejor el
sistema libre y en qué se diferencia del sistema diédrico a continuación se
explica paralelamente la proyección de la recta en ambos sistemas.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">La proyección de una recta
se reduce a la de dos de sus puntos. </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">En el “Sistema diédrico” las
proyecciones de los elementos a representar se realizan al menos sobre dos
planos ortogonales <span style="mso-spacerun: yes;"> </span>para determinar
inequívocamente las posiciones en el espacio de los puntos representados.
Estos planos se denominan plano horizontal de proyección H y plano vertical
de proyección V. A la recta intersección i de los planos de proyección se la
conoce con el nombre de “Línea de tierra“. A continuación se abate un plano
de proyección sobre el otro (normalmente el plano horizontal H sobre el
vertical V) para obtener las dos proyecciones ortogonales sobre un mismo
plano. </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8MikZZ5IKEFZM6sytFJv4utYxzE2a_ssz2aAQ-83ilDrODdAsmH7GOSTNR86UYlqIrtDaDxmEpNdr7O2wPX5lWxp9o2wDske1PRPkamwv_sYecLzIjaQeJLhG3WUU84a799kt72kq77Qk/s1600/Primera+imagen+-+copia.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8MikZZ5IKEFZM6sytFJv4utYxzE2a_ssz2aAQ-83ilDrODdAsmH7GOSTNR86UYlqIrtDaDxmEpNdr7O2wPX5lWxp9o2wDske1PRPkamwv_sYecLzIjaQeJLhG3WUU84a799kt72kq77Qk/s640/Primera+imagen+-+copia.jpg" width="640" /></a><span lang="ES" style="mso-ansi-language: ES;"></span><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES;"></span></b></div>
</td>
</tr>
<tr style="mso-yfti-irow: 7;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">El sistema diédrico se
basa en la proyección cilíndrica ortogonal. Por ello, al abatir el plano
horizontal sobre el vertical, las proyecciones de cualquier punto P, P’ y P”,
quedan alineadas en una recta que se denomina “Línea de referencia”. Las
líneas de referencia de las proyecciones de los puntos son siempre
perpendiculares a la recta intersección i de los planos de proyección.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<br /></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2GD4ClSV-b0tLREes_5S7lBCydO7uk2NDdqj_hMZnefAukeklfS4zL9KPGffKjbuDh38MGXfQ3PITJNxZBaNKPekyP0FsOJ_CFlX6gRxCkEucRBUGYZKQeL3_mgUBMMV-8vT6iW99Tvzc/s1600/DEF2+-+copia.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="382" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2GD4ClSV-b0tLREes_5S7lBCydO7uk2NDdqj_hMZnefAukeklfS4zL9KPGffKjbuDh38MGXfQ3PITJNxZBaNKPekyP0FsOJ_CFlX6gRxCkEucRBUGYZKQeL3_mgUBMMV-8vT6iW99Tvzc/s400/DEF2+-+copia.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 1</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 8;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;">Se
representa a continuación, según los conceptos explicados, una recta definida
por los puntos P y Q en sistema diédrico. Ver figuras 1 y 2.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<br /></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjDWkKKFfWTyUXi_ZEbShiGf2ebl8vb_arZRUCfl8dVxrte8Oz72mqqyVwSP6mjZ2AYO0lGpAZbhL9hFz_kfbwOi9TjOoZlG48IULIFACyfz_VL5jlkgf0mtgIfrHKBeN2dv67LOjW35kq/s1600/DEF2+-+copia+%25282%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjDWkKKFfWTyUXi_ZEbShiGf2ebl8vb_arZRUCfl8dVxrte8Oz72mqqyVwSP6mjZ2AYO0lGpAZbhL9hFz_kfbwOi9TjOoZlG48IULIFACyfz_VL5jlkgf0mtgIfrHKBeN2dv67LOjW35kq/s400/DEF2+-+copia+%25282%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 2</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 9;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;">La misma
recta definida por los puntos P y Q, representada sobre otros planos de
proyección H´ y V´ (paralelos a H y V), en sistema diédrico se representa tal
y como se refleja en la figura 3.</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES; mso-no-proof: yes;"></span></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb1dQTKoeipAqP7JebJbqHE5_c-cndIjSHhgShBnVH4SuiVm6y8JQLpXRRTCTwnyFDpdRC903MXfQ_3u2mjCr5EcoHJlXL8Yn-M3lzrnLO1YWw_e8UDv1aQAwAEfC74Kv3Ggi6u3vHu3rI/s1600/DEF2+-+copia+%25283%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb1dQTKoeipAqP7JebJbqHE5_c-cndIjSHhgShBnVH4SuiVm6y8JQLpXRRTCTwnyFDpdRC903MXfQ_3u2mjCr5EcoHJlXL8Yn-M3lzrnLO1YWw_e8UDv1aQAwAEfC74Kv3Ggi6u3vHu3rI/s400/DEF2+-+copia+%25283%2529.jpg" width="396" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 3</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 10;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Si se comparan las figuras
1 y 3 se observa que si la recta se proyecta <span style="mso-spacerun: yes;"> </span>sobre otros planos de proyección, H´ y V´, paralelos
a H y V, las <b style="mso-bidi-font-weight: normal;">distancias absolutas</b>
(z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2</span><span lang="ES" style="mso-ansi-language: ES;">, y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;"> e y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2</span><span lang="ES" style="mso-ansi-language: ES;">) de los puntos a sus proyecciones, <b style="mso-bidi-font-weight: normal;">dependen del plano concreto que se use
para la proyección</b>, pero la diferencia de distancias obtenidas entre dos
puntos de la recta o <b style="mso-bidi-font-weight: normal;">distancias
relativas</b> (</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y e </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">x) <b style="mso-bidi-font-weight: normal;">se
mantienen invariables</b>.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<br /></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo2guW00Pq5g1MASHDZ0JQeWVwGKSVyPoGcK4lLuEfElSwl_FMjqCIaMNaTTxS9qWGh1cXaYOwEPb-JtPY8Hm1EQ-RPjbfdpPBg0jX98hRjq-dWez9qz1sRDy4iJk9i4c1PAN7f6u9S3f_/s1600/DEF2+-+copia+%25284%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo2guW00Pq5g1MASHDZ0JQeWVwGKSVyPoGcK4lLuEfElSwl_FMjqCIaMNaTTxS9qWGh1cXaYOwEPb-JtPY8Hm1EQ-RPjbfdpPBg0jX98hRjq-dWez9qz1sRDy4iJk9i4c1PAN7f6u9S3f_/s400/DEF2+-+copia+%25284%2529.jpg" width="396" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 4</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 48.75pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 11;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">En el sistema libre la recta
definida por los puntos P y Q quedaría representada como se indica en la Fig.
5.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Se trata de una
representación más simplificada en la que no se pierde información sobre la
forma del objeto, como acabamos de ver.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">La representación se basa
en las tres coordenadas relativas (x, y, z) según la dirección de los ejes
coordenados del triedro. Desaparece por tanto la línea de tierra y sólo es
necesaria la dirección de los planos de proyección, y no su posición concreta
en el espacio.</span></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-ZY28qSHDOymkzQETYaQfOyHdF9UglI1obYUN7bD5cFjiHDNQCfBKg879Yle_Kd2DxjnJq7W5aInWVW_mjHBGwqd-2m5dRI-oQ5uFT0-cww4Jds0SU71JKG26ngALqSnNNe2mEmCJtdaq/s1600/Sistema+libre+-+copia.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="343" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-ZY28qSHDOymkzQETYaQfOyHdF9UglI1obYUN7bD5cFjiHDNQCfBKg879Yle_Kd2DxjnJq7W5aInWVW_mjHBGwqd-2m5dRI-oQ5uFT0-cww4Jds0SU71JKG26ngALqSnNNe2mEmCJtdaq/s400/Sistema+libre+-+copia.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 5</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;"></span><span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 12;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Para obtener la <b style="mso-bidi-font-weight: normal;">verdadera magnitud</b> <b style="mso-bidi-font-weight: normal;">del segmento PQ</b> <span style="mso-spacerun: yes;"> </span>se debe construir uno de los dos posibles
triángulos rectángulos en los que la hipotenusa es la magnitud buscada.
Dichos triángulos son el PQ-pq´-</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">Z y
el PQ-pq´´-</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y.<span style="mso-spacerun: yes;"> </span>Después<span style="mso-spacerun: yes;">
</span>se aplica el teorema de Pitágoras. Ver figuras 6 y 6a.</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 13;">
<td colspan="4" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 47.24%;" valign="top" width="47%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
<td style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 52.76%;" valign="top" width="52%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 14;">
<td colspan="4" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 47.24%;" valign="top" width="47%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN6ip9r7qImrhq0ay1lgLvBUjgnPgYrX025LZfWDal0Uw2Cz9oeWP-385SOTj2UBcGHJD4LJByc5YSbduUm0KuSwe8-VOgeckVZSVuiQ2guOuvAGI1ss4WZwbLM29yG-Y5rUCdy9Ok88l4/s1600/VM+03+-+copia.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN6ip9r7qImrhq0ay1lgLvBUjgnPgYrX025LZfWDal0Uw2Cz9oeWP-385SOTj2UBcGHJD4LJByc5YSbduUm0KuSwe8-VOgeckVZSVuiQ2guOuvAGI1ss4WZwbLM29yG-Y5rUCdy9Ok88l4/s400/VM+03+-+copia.jpg" width="276" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 6</td></tr>
</tbody></table>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
<td style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 52.76%;" valign="top" width="52%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Pi8D6bV0BjvjGK4ZwYNxD1R5DYUV0V18cadyZoPbMWRCz-OjH0JFIoN87dUGw4D42hFZwmMZlC6fPSmpa5Myyh8nadegy-RaVVFYCNElDil4rBeF_T1UeT0YUQdxnzhuftM1PuvOvrPp/s1600/VM+03+-+copia+%25282%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Pi8D6bV0BjvjGK4ZwYNxD1R5DYUV0V18cadyZoPbMWRCz-OjH0JFIoN87dUGw4D42hFZwmMZlC6fPSmpa5Myyh8nadegy-RaVVFYCNElDil4rBeF_T1UeT0YUQdxnzhuftM1PuvOvrPp/s400/VM+03+-+copia+%25282%2529.jpg" width="290" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 6a</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;"></span><span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 15;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">También gracias a los
triángulos antes descritos y al teorema de Pitágoras, <b style="mso-bidi-font-weight: normal;">se pueden obtener los ángulos α y β que forma la recta con los planos
de proyección</b>. Ver figuras 6 y 6a.</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 16;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 17;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">Tanto en
el sistema diédrico como en el sistema libre se pueden </span><span lang="ES" style="mso-ansi-language: ES;">etiquetar de diferente forma a las proyecciones.
Algunas biografías utilizan subíndices, otras tildes o números romanos.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="ES" style="mso-ansi-language: ES;">Normalmente a la
proyección sobre el plano horizontal se la denomina como “la primera”
proyección, a la proyección sobre el plano vertical se la denomina como “la
segunda” y a la proyección sobre un tercer plano ortogonal a los anteriores,
denominado plano de perfil, se la nombra como “la tercera” proyección.<span style="mso-no-proof: yes;"></span></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 18;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 19;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 20;">
<td colspan="5" style="background: #0070C0; border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="color: white; mso-ansi-language: ES; mso-themecolor: background1;">LA
TERCERA PROYECCIÓN EN LOS SISTEMAS DIÉDRICO Y LIBRE</span></b><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES;"></span></b></div>
</td>
</tr>
<tr style="mso-yfti-irow: 21;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 22;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">En determinadas
ocasiones es imprescindible utilizar la <b style="mso-bidi-font-weight: normal;">tercera
proyección</b> para que una recta quede totalmente determinada en el espacio.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Por ello
se explica a continuación como se realiza la tercera proyección para la recta
pq, definida por los puntos P y Q, tanto en diédrico como en el sistema
libre.</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 23;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">La
“tercera proyección” se realiza sobre un plano ortogonal a los planos
horizontal H y vertical V de proyección, denominado <b style="mso-bidi-font-weight: normal;">plano de perfil P</b>. Los tres planos, V, H y P, determinan un
triedro trirrectángulo, de tres coordenadas (x, y, z), que permiten restituir
la información espacial que tengamos representada (proyectada).</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Al
proyectar sobre un plano, la única coordenada que no se tiene proyectada en
esta proyección es la perpendicular a dicho plano.</span></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGrmJxLwjD9_8O3BJdowQO6nb2QpB9NxeJaYfchQ0p-9UiMKu3Vg35vnKA0K5cDzPIWd0pv5YRvR88BeGrAeOOVCRFRlRf8RbtJ9YgcZkZl1g-xPil-imdvIxi_vsSy70mLA-zfJ18b3pd/s1600/3RA+PROYECCION+-+copia.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="382" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGrmJxLwjD9_8O3BJdowQO6nb2QpB9NxeJaYfchQ0p-9UiMKu3Vg35vnKA0K5cDzPIWd0pv5YRvR88BeGrAeOOVCRFRlRf8RbtJ9YgcZkZl1g-xPil-imdvIxi_vsSy70mLA-zfJ18b3pd/s400/3RA+PROYECCION+-+copia.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 7</td></tr>
</tbody></table>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt; text-align: center;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 24;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Para
obtener <span style="mso-spacerun: yes;"> </span>la tercera proyección vemos
que los planos ortogonales del triedro comparten una misma coordenada dos a
dos, lo que sirve para obtener la nueva proyección. Ver figura 7.</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 25;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">Para obtener la
representación en diédrico de la tercera proyección:</span></b></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">Observando la figura 7 y conociendo P´, Q´, P´´ y Q´´, <span style="mso-spacerun: yes;"> </span>se ve que las proyecciones P”’ y Q”’ <span style="mso-spacerun: yes;"> </span>estan determinadas, pues éstas mantienen la
misma altura (z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES; mso-no-proof: yes;">1</span><span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">,z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES; mso-no-proof: yes;">2</span><span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">) respecto del plano horizontal que P” y Q” , y el mismo
alejemiento (y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES; mso-no-proof: yes;">1</span><span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">,y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES; mso-no-proof: yes;">2</span><span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">) respecto de plano vertical que P´y Q´. Por tanto, las
nuevas proyecciones, P”’ y Q”’ de la recta, se encuentran en las
correspondientes líneas de referencia. </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;">Ver figura 8.</span><span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt; text-align: right;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnPI1UhFP8dH7Uz0mrh0RVsfJ0OPATCmPb6GIu-jg9OcEKApsUb6RhzuEykANKEwZu2_CZchloGEid6e_vvn9rhPrcLCzq9n2Af_jHCk1VamFwkpZ2wIphTYCMwz1e17s02LIqDbJhT2wm/s1600/3RA+PROYECCION+-+copia+%25282%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnPI1UhFP8dH7Uz0mrh0RVsfJ0OPATCmPb6GIu-jg9OcEKApsUb6RhzuEykANKEwZu2_CZchloGEid6e_vvn9rhPrcLCzq9n2Af_jHCk1VamFwkpZ2wIphTYCMwz1e17s02LIqDbJhT2wm/s400/3RA+PROYECCION+-+copia+%25282%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 8</td></tr>
</tbody></table>
<div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt; text-align: right;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 26;">
<td colspan="2" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.56%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">En el
caso del <b style="mso-bidi-font-weight: normal;">sistema libre</b> la <b style="mso-bidi-font-weight: normal;">representación de la tercera proyección, </b>conocidas
la primera y segunda proyección, se realiza fijando uno de los puntos <span style="mso-spacerun: yes;"> </span>P´´´ o Q´´´. A continuación, el otro punto
se obtiene mediante <b style="mso-bidi-font-weight: normal;">las cotas</b> <b style="mso-bidi-font-weight: normal;">relativas</b> (</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y) <b style="mso-bidi-font-weight: normal;">que deben mantenerse</b>.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Ver figura
9.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
<td colspan="3" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.44%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUcYFUHVYMp-60Y19YRZuEk2kgNtqPA2Zw9BQ_EOY2sJE8RchnQXgxBuRmXp37mvDca-5G1mOu4V9VwOY9ijmyp3XkT8HxKes0e380v2jhQZK5CZloA0ZJxp1UHMsEO60tKFY-x7fpm_hN/s1600/3RA+PROYECCION+-+copia+%25283%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="365" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUcYFUHVYMp-60Y19YRZuEk2kgNtqPA2Zw9BQ_EOY2sJE8RchnQXgxBuRmXp37mvDca-5G1mOu4V9VwOY9ijmyp3XkT8HxKes0e380v2jhQZK5CZloA0ZJxp1UHMsEO60tKFY-x7fpm_hN/s400/3RA+PROYECCION+-+copia+%25283%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 9</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 27;">
<td colspan="5" style="background: #0070C0; border-bottom: solid white 1.0pt; border-left: solid #D9D9D9 1.0pt; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-bottom-alt: white; mso-border-bottom-themecolor: background1; mso-border-bottom-themecolor: background1; mso-border-left-alt: #D9D9D9; mso-border-left-themecolor: background1; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-left-themeshade: 217; mso-border-right-alt: #D9D9D9; mso-border-right-themecolor: background1; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-right-themeshade: 217; mso-border-style-alt: solid; mso-border-top-alt: solid white .5pt; mso-border-top-alt: white; mso-border-top-themecolor: background1; mso-border-top-themecolor: background1; mso-border-width-alt: .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="color: white; mso-ansi-language: ES; mso-themecolor: background1;">PROYECCIÓN
DEL PLANO EN EL SISTEMA DIÉDRICO Y EN EL SISTEMA LIBRE</span></b><span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 28;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid white .5pt; mso-border-top-alt: solid white .5pt; mso-border-top-themecolor: background1; mso-border-top-themecolor: background1; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 29;">
<td colspan="3" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.94%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Un plano
queda determinado por tres puntos no alineados, por lo que añadiendo un nuevo
punto a las proyecciones de una recta podremos definirlo. </span></div>
</td>
<td colspan="2" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.06%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMS1mOHSFk60k2kkRjZLs-GQMnPI0-4ALFhGmjOW_lBAecMLVIt3XeGxuwDZR74uj4r8IQO6NUn3TUVGkaqgFaLt60KMK_IJi9ABPGQBdjoM7heO48tzmuuYARXzfI8EPoUrZB_5bxg17h/s1600/Delta+x+copia+1.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="363" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMS1mOHSFk60k2kkRjZLs-GQMnPI0-4ALFhGmjOW_lBAecMLVIt3XeGxuwDZR74uj4r8IQO6NUn3TUVGkaqgFaLt60KMK_IJi9ABPGQBdjoM7heO48tzmuuYARXzfI8EPoUrZB_5bxg17h/s400/Delta+x+copia+1.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 10</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 30;">
<td colspan="3" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 30.94%;" valign="top" width="30%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Las
proyecciones diédricas de un plano quedan suficientemente determinadas con la
proyección de dicho plano sobre otros dos que formen un sistema diédrico, es
decir, que sean ortogonales. Lo normal es dar las proyecciones sobre un plano
vertical y otro horizontal, aunque es igualmente posible dar las proyecciones
sobre <span style="mso-spacerun: yes;"> </span>un<span style="mso-spacerun: yes;"> </span>plano vertical y otro de perfil.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">En la
figura 11 se ha representado el plano según los criterios del sistema diédrico.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
<td colspan="2" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 69.06%;" valign="top" width="69%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3hT5sZdRSBKHMD0NJPx1OoaYzJN353WrAeUwxMGTDI1rWlY3fbBrC6UmAB7J8ULkRYBIEdx7aWG-i_Q0zmBwx1PvV4DWxxpIYZd2AanTwSPDdIbjFPr_eO6zq6NqGLg7iaTPhBk2cPvf9/s1600/Delta+x+copia+2.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3hT5sZdRSBKHMD0NJPx1OoaYzJN353WrAeUwxMGTDI1rWlY3fbBrC6UmAB7J8ULkRYBIEdx7aWG-i_Q0zmBwx1PvV4DWxxpIYZd2AanTwSPDdIbjFPr_eO6zq6NqGLg7iaTPhBk2cPvf9/s400/Delta+x+copia+2.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 11</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 31;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Como se
aprecia, en el sistema diédrico priman las distancias absolutas (z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2</span><span lang="ES" style="mso-ansi-language: ES;">, z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">3,</span><span lang="ES" style="mso-ansi-language: ES;"> y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, y3</span><span lang="ES" style="mso-ansi-language: ES;">) frente a las distancias relativas (</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">x</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">x</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2 </span><span lang="ES" style="mso-ansi-language: ES;">) <span style="mso-no-proof: yes;"></span></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 32;">
<td style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 29.38%;" valign="top" width="29%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">La
representación de ese mismo plano, definido por los puntos PQR, en el sistema
libre es el representado en la figura 12.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Al igual
que en el caso de la recta, al tratarse de una proyección cilíndrica ortogonal,
la proyección del plano sobre dos planos paralelos de proyección, H-H´ o
V´-V´, teniendo en cuenta las distancias relativas, es invariable.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<b style="mso-bidi-font-weight: normal;"><span lang="ES" style="mso-ansi-language: ES;">En este caso se deben dar al menos dos
cotas relativas sobre cada plano de proyección con objeto de independizar las
proyecciones de los planos soporte de la representación H y V.</span></b></div>
</td>
<td colspan="4" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 70.62%;" valign="top" width="70%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhulvfipDNJl73wf8UtHckmEKpCKeVY1nYW2ym4D8eq6THgkALH6rclOhCeoqdmQIgbSmVKMv8swgpGt0rorJJd8DFGpU5Huc4dIBIMBoYNZFLoShV57vg5baX2TSEpUHKprNTe4feApNXf/s1600/Delta+x+-+copia.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhulvfipDNJl73wf8UtHckmEKpCKeVY1nYW2ym4D8eq6THgkALH6rclOhCeoqdmQIgbSmVKMv8swgpGt0rorJJd8DFGpU5Huc4dIBIMBoYNZFLoShV57vg5baX2TSEpUHKprNTe4feApNXf/s400/Delta+x+-+copia.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 12</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 33;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">El
sistema libre se basa en las distancias relativas (</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">x</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">x</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2</span><span lang="ES" style="mso-ansi-language: ES;">) y
prescinde de las distancias absolutas (z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2</span><span lang="ES" style="mso-ansi-language: ES;">, z</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">3,</span><span lang="ES" style="mso-ansi-language: ES;"> y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">1</span><span lang="ES" style="mso-ansi-language: ES;">, y</span><span lang="ES" style="font-size: 8.0pt; mso-ansi-language: ES;">2, y3</span><span lang="ES" style="mso-ansi-language: ES;">). </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 34;">
<td style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 29.38%;" valign="top" width="29%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">La
tercera proyección del plano se obtiene hallando R´´´, tercera proyección del
punto R, puesto que las proyecciones <span style="mso-spacerun: yes;"> </span>P´´´ y Q´´´ ya las conocemos (ver tercera
proyección de la recta). R´´´ se halla, tanto en el caso del sistema diédrico
como en el del sistema libre, procediendo de la misma manera que se ha
explicado para la recta. </span></div>
</td>
<td colspan="4" style="border-bottom: solid #D9D9D9 1.0pt; border-left: none; border-right: solid #D9D9D9 1.0pt; border-top: none; mso-border-alt: solid #D9D9D9 .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 217; mso-border-left-alt: solid #D9D9D9 .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 217; mso-border-right-themecolor: background1; mso-border-right-themeshade: 217; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 70.62%;" valign="top" width="70%"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEmc8iNCEYUZIa1TRntkj4jOYI_YqNoGv-lBNsXmJmHi8WC1Q5JE3Z1v2XKnX2m_mkXyISuUlWHQA4GXeRh0BoOZaxQ4QslgONhfnYTOs9L6SCTG4vBWeNb0jSIBSfZBbnFfkl-BLMfb-G/s1600/Delta+x+-+copia+%25282%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="327" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEmc8iNCEYUZIa1TRntkj4jOYI_YqNoGv-lBNsXmJmHi8WC1Q5JE3Z1v2XKnX2m_mkXyISuUlWHQA4GXeRh0BoOZaxQ4QslgONhfnYTOs9L6SCTG4vBWeNb0jSIBSfZBbnFfkl-BLMfb-G/s400/Delta+x+-+copia+%25282%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 13</td></tr>
</tbody></table>
<div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt; text-align: right;">
<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 35;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">La
tercera proyección del plano PQR en sistema diédrico es la dibujada en la
figura 14.</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 36;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMi3DoEWJv2P7P9Efk0lBbIC_-g7nWTjukw-eT5fbfyb5eBZ4xcSpKsISWlddqD2z2vJd-_mF0xN_4pgdmcnNstDzJQf0L7F7HwPKFxpFfbQ32tGdJ1bu1W4DJyQ1ZEjWZHXvBQZomeLYh/s1600/3+proyecc+plano+02+-+copia.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMi3DoEWJv2P7P9Efk0lBbIC_-g7nWTjukw-eT5fbfyb5eBZ4xcSpKsISWlddqD2z2vJd-_mF0xN_4pgdmcnNstDzJQf0L7F7HwPKFxpFfbQ32tGdJ1bu1W4DJyQ1ZEjWZHXvBQZomeLYh/s640/3+proyecc+plano+02+-+copia.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 14</td></tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br />
<span lang="ES" style="mso-ansi-language: ES; mso-no-proof: yes;"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
</tr>
<tr style="mso-yfti-irow: 37;">
<td style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 29.38%;" valign="top" width="29%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">La
tercera proyección del plano PQR en sistema libre es la dibujada en la figura
15.<span style="color: red;"></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">De nuevo
la proyección R´´´, conocidas la primera y la segunda proyección, se obtiene <span style="mso-spacerun: yes;"> </span>mediante <b style="mso-bidi-font-weight: normal;">las cotas</b> <b style="mso-bidi-font-weight: normal;">relativas</b> (</span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">z, </span><span lang="ES" style="font-family: "greeks"; mso-ansi-language: ES;">D</span><span lang="ES" style="mso-ansi-language: ES;">y) <b style="mso-bidi-font-weight: normal;">que
deben mantenerse invariables</b>.<span style="color: red;"></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
</td>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSHQ8UGvcwGVtzm6Ld1Caa9rweD5-YdHR7CBQU2BewY1BZvSZ8fSVdhS0yxKLC1ipYDGmtSCvyIY3_o9k1bsJiUYMTqFDgUghuMJFpVIqubDZS93wJNRhAB2Ll8DBp-nndjbcNS_LRhdDo/s1600/3+proyecc+plano+02+-+copia+%25282%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSHQ8UGvcwGVtzm6Ld1Caa9rweD5-YdHR7CBQU2BewY1BZvSZ8fSVdhS0yxKLC1ipYDGmtSCvyIY3_o9k1bsJiUYMTqFDgUghuMJFpVIqubDZS93wJNRhAB2Ll8DBp-nndjbcNS_LRhdDo/s400/3+proyecc+plano+02+-+copia+%25282%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 15</td></tr>
</tbody></table>
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<span lang="ES" style="mso-ansi-language: ES;"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 38; mso-yfti-lastrow: yes;">
<td colspan="5" style="border-top: none; border: solid #D9D9D9 1.0pt; mso-border-alt: solid #D9D9D9 .5pt; mso-border-themecolor: background1; mso-border-themecolor: background1; mso-border-themeshade: 217; mso-border-themeshade: 217; mso-border-top-alt: solid #D9D9D9 .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 217; padding: 0cm 5.4pt 0cm 5.4pt; width: 100.0%;" valign="top" width="100%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 127.6pt;">
<span lang="ES" style="mso-ansi-language: ES;">Recurso
didáctico: <a href="http://piziadas.com/dibujo/sr">http://piziadas.com/dibujo/sr</a></span></div>
</td>
</tr>
<tr height="0">
<td style="border: none;" width="219"><br /></td>
<td style="border: none;" width="9"><br /></td>
<td style="border: none;" width="3"><br /></td>
<td style="border: none;" width="122"><br /></td>
<td style="border: none;" width="394"><br /></td>
</tr>
</tbody></table>
<br />
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<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com2tag:blogger.com,1999:blog-1732523761923805891.post-37561929429061276232016-04-10T10:49:00.001-07:002016-04-10T11:17:04.565-07:00ENUNCIADOS_INVERSIÓN_EJERCICIO_02Dados los puntos P y Q y sus inversos P1 y Q1, halla:<br />
<br />
-Centro de inversión (I)<br />
-Circunferencia inversa de la concíclica formada por los 4 puntos dados<br />
-Inverso del punto Z<br />
<br />
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<br />
<br />
Halla después los mismos supuestos estando el punto Q=Q1 ahora en la siguiente posición:<br />
<br />
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<a href="http://planolineapunto.blogspot.com.es/2016/04/problemainversion02.html">Pincha aqui para ver la solución!!!</a><br />
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Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-61489108167470524692016-04-10T10:33:00.002-07:002016-04-10T10:41:58.159-07:00SOLUCIONES_INVERSION_EJERCICIO_02
Utiliza la barra de navegación para ver el ejercicio paso a paso.
<iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/kPDrd9s4/width/650/height/400/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="650px" height="400px" style="border:0px;"> </iframe>Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-21410726551866961462016-04-04T09:30:00.001-07:002016-04-04T10:27:21.207-07:00TEORÍA INVERSIÓN<!--[if gte mso 9]><xml>
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<b style="mso-bidi-font-weight: normal;">INTRODUCCIÓN:</b></div>
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La inversión es una <b>transformación que conserva las relaciones angulares (es conforme)</b>. </div>
<br />
Su principal aplicación en geometría es la determinación de problemas con condiciones angulares entre los que se encuentran la resolución de ejercicios con tangencias.<br />
<br />
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<b style="mso-bidi-font-weight: normal;">DEFINICIÓN:</b></div>
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La Inversión en Dibujo Técnico es una transformación geométrica que cumple que:<br />
<br />
1-Dos puntos inversos (A, A1) están alineados con un punto fijo (O) llamado Centro de Inversión. Por ello la inversión <b>es una transformación con centro</b>.<br />
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<br />
2-La relación entre las posiciones relativas de cada punto y su transformado respecto del centro de inversión se basan en el concepto de potencia.<b> El producto de la distancia de un punto al centro de inversión por la distancia de su inverso al centro de inversión es constante (K) y se llama potencia de inversión. Por lo tanto: OA*OA1 = OB*OB1 = OT*OT = K </b></div>
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chxxx3nPYJCKUZju9jBeQqFdGMNH0IJABSTgogKWqtWrerqFtgmSIJ4tSf50FaNjviuWbOGwXkhRygBgGJYvXq12yqgNXmSJRBK/G6sGpynmpF27dqxVRNyhBIAKKIFCxa4nhe9e/fmVEeyFRBKNDhP22V0Y80uhBIAKCS9Q58+fbp9+umnNERLlXxCSezgPLqxZh9CCQAUgl4UNb9G9SNdu3ZleFua+N1YFy1axOC8LEYoAYAEffjhhzZx4kS79NJLoztQLwP8wXmarNy9e3e2arIYoQQAErBy5Up7/vnn3XZNqutH1J5eQ+O2bdvmbps3b7bt27e7awcOHDh0XV8nuu5/HqtMmTJ26qmnHva5bvpcL/AnnXSS+7OULVvWqlSp4h4L0lFmf3Ce6kd69OjBVk0EEEoAoAA63aHZKX369Elq7wu96OoYq27r16+3zz///NBNQcEPEQoOChAKErHhwg8Quh4vTOzbt8+FF4kNOv71r776yq1C7N692/0/dU2/brVq1dxHdaOtW7eua0Km0JIu/laNCom1ItW+fXu2aiKCUAIA+VD/EW3X6EVfRZXFOW6qQLBq1Sp3WmfdunUuiCgc+C/6p59+uv361792L/76qPCRCQopCidanVFQ8n+vWqHR71O/X03YPffcc11wSTZ/cJ5qdrp06cJWTcQQSgAgDnUHffDBB13vEfUgKWwzLoWQFStW2CuvvOLe8eu+XtAvuugia9iwoftcAeSoo47y/otgU1DxV3X0Z1LA0uqMhg36IaU4qyn6+1G/F23VqICYni/RRCgBgDz82SlaHWnQoIF3tWB6oV68eLH7b7XSoOChrYeLL77YfZ6p1Y9UUUDRn3fevHnuz64Vng4dOrg/r4JXbOCaO3euDbvjDtu4aZNVq1TJho4aZZ1zwsf+/fvdVo1WkNSJVQGQrZroIpQAQAwVViqUaH6NaiuORNsvejFWCHn22Wdd6LjyyivdakjTpk2zLoQUZOnSpW4VRX8XqmFRqFNI2blzp9183XU27euvrcXBg/Zmztd2O/pou/7OO+2r3bvd37NO1ZQrVy73F0JkEUoAIIeGuE2dOtX1ISlooJ6CiL529uzZbstCKwPactBqCHKpNkXh5KWXXrIP33vP5vz4o7WMeblRMPntscfa/NdfdwW1gBBKAESeOrOqZbkChqbLxqsfUc3DE088YU8//bS7/9vf/taNxU9He/mPPvrILrvsMndCRr8H1XGEyYlHH21f79vn3fvJ0SVL2ncHDnj3AEIJgIjTaY9Jkya5WgYdP40NJDpxoloItZTX6ohCiObcpHtF5IorrnBdTLUl1KlTJ1cMGiaNzjjDxmzcaC28+6KVks5lytizixa5PxcghBIAkeUP1MtbP6K+HTp5ozCilZDrr7/ebdFkqkbkhBNOcHUZYTmpE+uTTz6xu+++25Y8+6w9/cMPLpi4mpKcP0uHa6+1172j0T179rR+/foFqnkb0o9QAiBy/PqRL774wm655ZZDL4Q69nrfffe5YtfWrVvb7373O3eKJNNKlChhYXuq/vbbb23OnDnuWLQCnf7O77vxRlv32WdWrWxZG57z99w5J+yJTvCMHTvWrUZdmxNUbr31VtcbBtFDKAEQKToVMmHCBHfSw2+IpqJMhRGdHtHpmZtvvjkljcGKKmwrJQoiCnbqNaI5QYmufugY9bBhw9yWmbbKhg4dWqzeJwgfQgmAyFi7dq3rFqp37qof0fj70aNHuzCiWpEbbrjBtXcPGr1A68W9UaNG7mNQa0o0sFDHow8ePOgCX40aNbxHCkcFvVo50b8VKyfRQigBEAlq8KUaEp2uUevy22+/3W0bqJ5k8ODBga5l0Ombdu3auVk1Tz75pAtVQaKtGs0HUujzA19hO+DGoxNPDz30kCtEVjjRygk1J9mNUAIgq2m42zPPPOPexevd+5/+9Cf3DlzD9fQOPIgrI2Ghv1tt1SiQ6ASNVnFS0Y1VtT6q/VGo1L+ZQmQYi35RMEIJgKylRmiqH9ELmF4sR4wYYZdccomNHDkyUDUjYaSQp3CnmhyFvWROT86PhgP279/fraDo3zBs/VpQMEIJgKykhmjjxo2z0047zV588UUXSh544AE36RZFp0CglRHVtSgUqJg1GVs1haFtt+uuu84NARwzZgzFsFkkvd9JAJAGaoimQKKVEvUb0VyVRYsWEUiKQVs1qstRXUelSpXs3nvvtfPOOy/tgUR0XFv/xip+PeOMM+yee+5xvU4QfqyUAMgqOoq6fPlye/XVV10XVC3zUxxZPBs2bLDnn3/ehQDN+AnSSRgd577mmmtc910VATN/KNwIJQCygk6AaHtGx3zfeecdV9CqUIKi01aNBurpiK7CSDrm/BSFAsn999/ves2oEPa2226jEDakCCUAQk/bNGq6tX79eqtVqxarI8WkrZqXX37ZnXbR8V6dqilVqpT3aHBp1URHvvVv7w9YRLgQSgCE2rvvvutWRdQNdMiQIa7eAEWnWg2dqqlevbpr2ha2pmVaNVEdkZqvqQhWJ4MQHoQSAKGg1uPDfv972/jxx1atQgUbev/99r+/+IXbXti7d6899thjdP0sBs0BUj2OVp26detW5G6sQaFVE63w+EfAMzVMEYVDKAEQeAokA6+6yqZ9882hKbNdSpa0GvXrW4fu3W3gwIHUEBSRanEWLlzoWu23adPG2rZtm5ETNamgac/63lB/Ew0HZDsn+AglAAKvUZ06Nub9910g8SmYXF22rG3etSv3AgpNbeGnTJliZ555pitk1ZDCbDRq1Ci3naNgot4mCC5CCYDAK3fssbYr5x19XkeXLGnfHTjg3UOiduzY4cKIClqzYasmEWq4piLY66+/ntM5AUYoARB4jXLeyf+/jRutZc6LqE8rJb0qVLD3t2/PvYAC7d+/303xfeutt1wRa/PmzbNmqyYROtqsLSqtlkycOJE6kwCioyuAQNO7+bMaN7YrS5a0pd41BZJupUvb8LFjcy+gQGoop8nIP/zwg5sBlKxJvmGimhL1sFGtiYpg9RHBwkoJgMBSEeadd97pChWbNGli83Pe5a/bssWdvhk+bpx17trV+0rkRzNqdKrm4MGDrt1+tWrVvEei7cYbb3TFvX/5y1/4OwkQQgmAQNKLqY5yqkPrQw89ZPXr1/ceQSL27NnjBuep74i2aho1ahS5lZGCqJ+JvrdUAEt7+mAglAAIHNU8PProo7Z161Z7+umn6T9SSJr7o9URTfC9/PLL6W57BGoUp1UTdbBt2LChdxWZQigBECh6d6++JGp+NX/+fCtbtqz3CAriD85TAadO1VStWtV7BEeidvo6maOBfnQEzixCCYBAUP2I2sX//e9/t08//dTt9bNCkhgd8dUWhLa61G+kXr16bNUUko4Md+nSxWbOnGkXX3yxdxXpRigBkHHapnnkkUfs448/tp07d9pf//pXjmsmQCdpdKpGqyNNmzZ1L6qlS5f2HkVhacVEK0xaMVF7eqQfoQRARmnLYfLkyW5M/vbt2907fgJJwbS9pUm4FStWdKsjlStX9h5BcfgrJqoxoftr+hFKAGSM3pm+9tprLoxotURbNgSSI9PAPG0x6HRSjx497KyzzvIeQbL4NSb6fiSYpBehBEDaqSGaOovq3b62bDShlhWSI9Pfmd69L1q0yFq0aOEG57FVkzr+Vo5OMqlGB+lBKAGQVtqmGT9+vDsZokAyb94890JLUWv+1GtER1erV6/ujvhWqFDBewSppL/zW265xVauXEmDtTQhlABIm08++cTVjzRr1sy2bdtm9913n3vCJ5DEpwCnfiOa2XL11Vdb7dq1vUeQLmqwNn36dLdiwvH01COUAEgLhQ/1IOndu7dt3rzZBg4c6J7oeQf6czpVoxUknaxp1aqV26rhiG/mqLmaRh2wxZh6hBIAKaVaCB1ZVf3IoEGD7J///Kd7kdUTPB00f07dbBXeatWq5drDn3jiid4jyCSdyBEVGR911FHucyQfoQRAymj+ysMPP+yOrWr74csvv3QzWDQ2vmPHjt5XQXT6SDUMWiXREd+aNWt6jyAI9u3bZ+edd5516NDB7rnnHu8qko1QAiAldKJGBa1t2rRxY/L1pK6PF110EU/qMdTJVu3033jjDVfEqmnIbNUEk2p7FEwee+wxur6mCKEEQNJpC0IFmrF9NNT3QfSEzvJ3rhUrVritGh051VbNMccc4z2CoFqzZo3bflQ9FIXHyUcoAZBUs2fPtrffftsVslaqVMld0wkGTf3VXBsKBc01PlOflpIlS7ptLbqxhou+n6dOneqKt5nAnFyEEgBJoW2ISZMmuZqIfv36HSrQ9N9Z0ush9+9IK0jr1693WzWNGzf2HkHYXHPNNW7FT63+kTyEEgDFpn4aEyZMcFs1KmD1ayJ2795tZ5xxho0cOdKuvfZady2KdAJp2bJlbqumefPmdumll9KNNeT0va3vd31va7ULyUEoAVAs6jaqd4vdu3f/2RFfvZvU8rZO20SVjkLrVE358uXdixfdWLPHm2++aZ06dbJ33nnHqlSp4l1FcRBKABSZ5oOoWLN///4/q4t45JFH3OpJVOtI/G6saqWvMMLgvOx0//33u/ogDZakXqr4CCUACk11I/6kWs0GyVvsp46t9evXdzNtojZl1R+ct2TJErqxRsCBAwfcMeH27dtz1D0JCCUACkWj83X6QMvVWgGIVxuh3iTaytF+e5TEDs7ThFm6sUaDtugUwrWNU7duXe8qioJQAiBhevLVQL0LL7zQ3eKtAPjbNnqCjspxyR07drgwsnPnThfU6F8RPaNGjXLbOPq+pw9P0RFKACREzaI0r0b1I/m1QNcUYLWR19dFYdvG78aqkzU64quTNWzVRJO2cS644AI6FhcToQTAEal+ZMaMGa5+5KabbrKTTz7Ze+Tn1EZeYSQK2zbqWqt3xnRjhU8riaovUXE306+LhlACIF+qH1FDNNVGqE38kXprTJkyxcaOHZv1p21iB+fp74RurIilTsY6eaVCcBQeoQRAXJ9++qmNGzfOWrRoYZdddtkRtyX0JKwmadm8bbN//37XQl8rJAzOQ340GVvHvx944AEmYRcBoQTAz6j3iLYm+vTpY2effbZ3NX96d6jiPj0RZyN/wKBebNiqQUEWL17sfiZ0Goui18IhlAA4jF58V69ebQMGDEhoa0KzbXQEWNs22dbV0t+qOXjwoOtYS50AEqWi1w4dOtjvf/977woSQSgB4Kh+RMd91fxLgSTR47ya46ITBzfccIN3Jfz8rRqtGHXt2pWtGhTaunXrXFj/8MMPmSRcCIQSAPbFF1+4+hFNrVW9RKIvwEuXLrXrrrvO9WYoW7asdzXc/FM1DRo0cH8XbNWgqFQIrdNqY8aM8a6gIIQSIOL0IqwtCq0ING3a1LuaGB0B1qqK6izCjlM1SLZt27a5Tq+qLTnSUXr8hFACRJi2KJYvX26DBg0qdL2EivmGDBniBpGFuZhPJ4dmzZrlekwomKn5G1s1SBY1Utu7dy+rJQkilAARpNUAtYJX7US/fv2KNKNFJ1GGDx8e2mOP/uA8dWRt1qyZq41hqwbJ5h+X1xYnhdIFI5QAEaP6EQUSDY3r0aOHlSpVynskcc8++6xrlLZy5cpQrpJoOV3NrcqVK+dm1VSqVMl7BEi+G2+80Xbv3m3Tpk3zriA/hBIgQrRFoUCiAk7VgxSV9smHDh0aulUSvWtVEata5tMADeny+eefu5XF999/30499VTvKuIhlAAR4dePqCFanTp1vKuFN3fuXLvllltC1RiKrRpkGidxEkMoAbKc6ke0bKwJvgUN1EuEmkL17NnThZsw8Ldq9OfWKaGqVat6jwDps3nzZvezQ9+SIyOUAFlM2xUPPvig67Ra0EC9RKxatco6derkXuiD3pfE36rRUV+dqkmkXT6QSm3btrVWrVrR5fUICCVAllL9iCb8JjJQL1HXXHONe3EP8pOqThRpq2bJkiV28cUX24UXXlikYl4g2XSMXkWvGsnATJz4CCVAFnr11VfdKkH//v2TtkKgYr2aNWvaZ599FthGUP7gPJ2m0eoIDdAQNOqDo7oSvVnAzxFKgCyi+pEZM2a40yWJDtRL1IgRI2z9+vWuPiNoduzYYc8884z72K1bN3fSAQiiJ554wq3iPfnkk94VxCKUAFlCA/VUP1KmTJlCDdRLlPqaPPbYY9a6dWvvSuZpq2bevHlucF779u3dMWeO+CLI9uzZ41YcaT0fHz+9QBZQ/Yj6hpx55pnuuG6yA4kG72kPPEhLzmrcdvvtt7sn+XvvvdcVEBJIEHT62VR/H20z4udYKQFCTqsE2lLRtkV+A/U0Qt2ncKF214MHD7bTTz/du3pkOrnzy1/+0s3xyDQdbdZWzbfffmvdu3cvVs8VIBPefPNNV/CqYI3DEUqAEFP9yOrVq13AONJcDYWSRYsWuc/1I79w4UJXCPv444+7a0eio7WnnXaa60aZydkdCiF6d6k/b4cOHax58+asjCC0NA9Hbybq1avnXYHwEw2EkOpHVMGvOTbDhg0rVFgoUaKEXXTRRa4oNBEa5686kkwGEp0muvXWW10X1j/+8Y/UjiD01IBw6tSp3j34WCkBQkZBZNy4cVa7du2EB+rFrpSIVkq++eYb1+G0IDrCeOedd2Zkzo1OEWlFp2TJkm5wHkd8kS3WrVvnwrWO2Ks4HbkIJUCIqGJfA/XUg6MwA/Via0p86mGioXRHsm3bNnfqZteuXWl94tRKkLZqNm3a5H6PjRs39h4BsocGWz7wwAP0LInB+icQEjr6qhk2gwYNKtKEX62U+Lc//elPCfUbUTBQV9R0BRINztOf86677rITTzzRnaohkCBbqTbqpZde8u5BCCVAwKkh2vjx491yr479JuO0ifok7N2717uXv+nTp1vv3r29e6mlVSAd8f3ggw9syJAhbmupuLN6gCC78sorXc3WgQMHvCsglAAB5heyqsBTE361epAMWo0oKNxo60ZBKNVLyzrdoxk9OkmkuhH9OStUqOA9CmQv1YWpb4kGXSIXNSVAQGnlQNX5WjHIr/9IovL2KfGbrFWsWNG7+nPPPvusWynRcLtU0AqQwpFabqvxmSaosjKCqNHqoL7vg9ADKAgIJUAA6cV6/vz57nRNpmoqunTpYueff77rgZJsGpw3a9YsV0SrQlZWRhBV6pbsTw4GoQQIFM1ymTJlitu20fwaTbvNlOOPP94+/PBDO/XUU70rxafeKNpD3759u9uqYXAekPuzpuaEVapU8a5EFzUlQEDo2K0ag2lbQ4WemQwka9ascXvdyQokfjfW4cOHu9b2I0eOJJAAnoYNG7rW8yCUAIGglRF1aNWTk478Zrq2YvHixUlrlqbZPHfccYcraB0xYoSb5ks3VuAn+plQbRXYvgEyTvUV6hmioXdnn322dzWz1AdF20eJdHzNj9+NVask2qrRSQMAP6eVSRV6681J1BFKgAxRo7DZs2fb2rVrrV+/fhndrsmrOHvc/lbNO++844pYGZwHFCwVNVxhxDMFkAEqaH344Ydtw4YNbmsjSIFEvUlUT1LYQKKQpcF5Omqsuhht1TA4D0iMtm611Rl1PFsAabZ161a7++677eSTT3aTb4PWm0NHFNVavjA2btzo/kyvv/66O0KsLrDJavQGRIEmd1NXQigB0kqdG1XQqh4gqrNIZMJvumk76ZxzzvHuHZnfjVVt8NUATas+amEPoHDq1avnVimjjpoSIE1UP6KVBNWP1KhRw7saPOedd54LTkfqIqutGnV6VYM3NXdTQaxa4QMoGgV8Bfovv/zSdV2OKkIJkGKqH5k8ebLt27fP+vfv7+o1gkz1LSpyLVu2rHflcGp/rwZoKszTiaHKlSt7jwAoDv3sqUA8yk3U2L4BUkj1IxqoV65cOVdrEcRA8vnnn1ufPn1cq/cSJUrYzp077brrrrPNmzd7X5FL7+QmTJjg5vFceumlbquGQAIkT926dd3x4ChjpQRIEdVmqGV89+7d3ZZIEKlJmsanly9f3k466SQXmnSkV+3gtYz8+OOPuyZq/laNTtO0a9eOrRogBXRyTT+Ht912m3clegglQArMmTPHFi5c6FYggtIQLS+tkNSvX9+qVasWd6vm3//+tzuyfNVVV7mvUWEuKyPhpRNSCsn6qGDph1EEh/59XnnlFXv++ee9K9HD9g2QRKofefDBB90qydChQwMbSGT06NHuRSm/2hHVjFSsWNH9WXR0mUASXv/85z/d3KGuXbu6wKygOXbsWDeNGsHx61//2rZt2+bdiyZCCZAkX3/9tQskOuarF3H1IQmyWbNmFfhOWXUmWi1BuD399NPWo0cPa9SokasbUg8Z1Thp1QTBoW6un3zyiXcvmti+AZJABa0qAlWvjrB0MdWLU+vWrb17+VPdCU8T4dahQwf785//HLhGffg5rVBqBk7QT+mlCislQDFpoJ6Wwrt16+ZCSVjaqms7Zs+ePd69+FT0SmfW8Pv+++8JJCGh1ZIob+EQSoAiUgMxTcFVa2gdjz3rrLO8R8KhU6dObsvpSHQMuFmzZt49hNWxxx5r3333nXfvJ/GuIbMUSlSEHlWEEqAItIKg+hHt/2pvPuj1I3mpTuTgwYNu20nFufHs3bvXhZJx48Z5VxBW//Vf/2XLly/37uXasmWLa+aHYFHhuX7uoopQAhSSXsh1suZXv/qV6ysQpp4d6j+ikKEVnkGDBtmLL75omzZtsu3bt7sQIgpc//M//+PGqE+fPt2dCEC4aQyAes68++677v5nn33mTl/pOoKldu3aP2tcGCUUugKFoPoRtVgPcv+ReLQaogZoeresbqzNmzc/VPuipeK77rrLncZRbxI1b1Kx7siRIwkkWUSBROMOPv30U1cndMUVV9jll1/uPYqguP/++92bBM2fiiJCCZAg9XdQKNGSd5h6dqxevdqtjKjmRS9C+a3saI7N+eef7wIXgMx44oknbNmyZTZt2jTvSrSwfQMUQCdUdNxXdRhq/xyWQKJ3xFqiV5jSVo06sh5pq+nAgQNWpkwZ7x6ATNDPoIZ3RhWhBDgC1Y+oE6Y6m6p+JAy9A1QTopUR1Y5o5s6QIUMSClI6hqjKfwCZw+kbAHFpZUT9R1SDoYLAMPQfUc2IjifLH//4R3ecN9HfN6EEyDyd5OP0DYDDLFiwwA3H0rZH06ZNvavBpZMyCiGqeVGLe804KeypIG1TRbWLZNjpnbVqnf7zP//TderVeIB+/fpF+hRHWOlnMMrbNxS6AjG09aETCjqtoif1oHcz9bdqFEoURIpzIqh69er26quvuonACA8FaHUT1qmpU045xb2o6fuiZMmSrhfJo48+apdccon31Qg6BUxtu+rYdhQRSgCP5k2MHz/eatSo4YaXabBeUKmb7MKFC91Nx3cvvvjiYv9+oz5zI4z0AnbmmWdarVq14k57Puqoo+wf//iHO83B8e5w0CpJuXLlItttl1AC5FD9yMSJE139yIUXXuhdDSZNdtXqSKVKlaxLly7uCSwZtOzP00G46Ij32rVrXSO//KimSNOgZ86c6V1B0EX5Z5FQgsjT8reOzWq7Jsjza1T8NmPGDNfgrHv37lazZk3vkeQglISPAqk6gB5pdUurauvXr4/0kLewIZQAEaQna7VR1/waBRKtPATRDz/8YPPmzXMna/TOuEmTJik5CUQoCR/9m7Vu3dq7l7/FixfzbxsihBIgYrTqoIF6VatWtZ49ewZ2rLtO06j9u1Zw2rdvn7StmngIJeGjQuw6deoccaVERduab8RKSXgQSoAIUadTBZJWrVpZ27ZtA9l/RIPzNGNHRW9aHdESfaoRSsJHBc46eXWkmhIVTJ522mnUlIQIoQSIiJUrV7oiUbVcb9iwoXc1OHSUc/78+fbGG2+4glvd0hWaOH0TPupDomPgdevWtRNOOMG7+pPvv//erZK89tprnL4JiaifvqF5GiJDRaLPP/+83XTTTYEMJNqq0bTer7/+2u699173LjidqzhR7yQZRgoa+r5WIetHH31ke/fuddcVbjVpVie1HnvsMQJJiOhnUD+LUcVKCbKenqC1XaNBV7179w5cQzTN19FWjQpa+/bt67pxZgLN08Lrn//8pyvWfuedd+yrr75y77TVv0YDGQkk4aLCe/3bffzxx96VaCGUIKupfkQTfhs3bmwdO3YMVP2IwtILL7xgq1evdttJDRo0yOjvT8W0qjvQVgCAzFi3bp3rP/T+++97V6KF7RtkLTVEU4dWFYrqFqRAsmLFCjc4T/Ubmlmj7aRM//40jI8TGkBmRX37hlCCrKS+HtOmTXPbIVolCQrNIlEIefvtt23w4MEuLBV2cF6qEEqAzNPPYJUqVbx70UMoQVZRXYa2a/Sir5WIZHc9LSpt1aggcerUqdasWTMXSIJWu6E5KVGeTgoEgX4GVf8WVYQSZA319hgxYoRbeVAgSWWjsUSpa6yKR/X7UYM2/f6aNm0aqK0kH6dvgMxj+wbIAqpY17aIGqL16tUrEB1atVVz991326pVq2zo0KHWtWvXQIYRX8WKFd3JDQCZo6PcJ510kncvegglCD01RHv44YdtwIABbmsk09RnRNs02kbS4LxbbrklEKs2BdHRUfW1AJA5+hmM8jFuQglCS1sjqtNQUate+DNdP6Lfj34v2qKpXLmyjRw50s0lCQu2b4DM2717N83TvM+B0NBqhFYiVBCmplGZPsGidzdqgKYGZJdeemnGGqAVhwJJ/fr17bPPPvOuAEg3vbl6+eWXI7taQihB6Kgh2qRJk+y8885zk3MzWaehF3I1QNPMGB3v1RySMNP8m127drmTOADSL+ozqNi+QahoPsy4ceOsW7dubkUiU4HE36pRca22alTIGvZAIupVQl0JkBn62Stbtmykh2ISShAaWpGYM2eO3Xrrra4leqa89957dvvtt7uR8Rqcl8lwlGz16tUjlAAZosZpUZ89RShB4GlVQu3idVRuyJAhVqlSJe+R9FIfFK3SqHakT58+rgFatr2jqV27Nl1dgQzZvHmzW62MMkIJAk01Gxrnrxd/BYFM9B9Rl1it0gwfPtwVgupUTVA6xSabtqA++OAD7x6AdNLP3jnnnOPdiyZCCQJr7dq1bvS6tkcy1RBNNSwKRTrto6O+GimeLVs18Wj7Zs2aNd49AOmkn72oT+nm9A0CSUWkS5cudQ3RMrHHunXrVrdNo1USdWLN1pWReLQ9prHpKrgDkD762XvnnXciPZCPUIJAUQjQdF8diVMgSXcTIQ3O01aNnhh0xLd58+ZZvTISj45ajxkzxs3oAZAe2qrWm58vv/wy0kfy2b5BYOiHctiwYe5zDbBLdyDR4Dyd7BFtG2X7Vk1+tHzMFg6QXpqRpZ+9qPcIIpQgEDZs2OB6figIqKC1VKlS3iOpp8F5+n+//vrrdtttt1mPHj0y3iE2k1Ts+u6773r3AKQD9SS52L5Bxq1YscJtmfTu3Tut/UdUvKr/7/r1691WTZMmTSK5MpLXunXrrE2bNm4LDUB66A2Ztqw7d+7sXYkmQgkyRv1Hpk+f7pqQqedHuubF6P+r2RILFixwNSPt2rWL9MpIPGp1rX+XqPdMANKFn7lcvC1ERmiVQlsmCghq0Z6uQKJupXfffbdbDdBWjd6VEEh+rmHDhm4FC0DqaetGvZh4E0AoQQZooJ6CiMb6a8smHf1HVESrIX5Tp051fU9U0KqZNYjvoosusiVLlnj3AKTS4sWL7eKLL/buRRvbN0grv35EvT909DTVdMRYPU8WLVrk9mwVSDLRhC1s9M6tbdu21JUAaUA9yU8IJUgLbdM888wztnr1arvlllvSMr9G3VhnzZplFStWtKuvvjptW0TZgj1uID1OOeUU+/vf/x7ppmk+QglSTvUj2jqRvn37Wrly5dznqaLBeerGqnf5Ot6byYnCYaZVpfbt21u/fv28KwCS7c0333RjNNRFGdSUIMU++eQTNzOmRo0aboUklYHE78aqQtZf/epX7v9LICm6q666yl566SXvHoBU0ClAbWcjFyslSJmVK1e6FYtu3bqlvGW5X6ui0fvqOcJWTfF9/vnndsYZZ7i212XKlPGuAkgm/YxNnDjRWrRo4V2JNkIJks6vH9GU31QP1FM31ueee85tEaluhJWR5NLfp+bgcDIASL7Nmzdbo0aN3FYzwT8XoQRJpS2U8ePHu1MvqkVI1fya2MF5esHUSRG6sSbfqFGjXLicOXOmdwVAsujn64MPPnBDSJGLUIKk2bVrl40dO9adrFFBa6rm12hwngKJ3sVra+jEE0/0HkGyqSZIf8/6t436oDAg2XQUWD2TWIn8CaEESfHee++5tN+xY0dr1qyZdzW51HRN/w+twmirRvUjSD3teT/wwAM8cQJJpMBfv359+/jjj61s2bLeVRBKUGwLFy50pzS0XZOKmo49e/bY888/70Z765jqhRdeyFZNGrGFAyTfI4884qZxs3VzOEIJikwFraoaV5HWoEGDkn7iRb++TtUokJx55pnu2Fyqe5zg53QKp2bNmvbZZ5+lrEYIiBp1tB45ciSnbvIglKBI1KBMgUT1Iz179kx663Zt1WhOzcGDB9mqCYBOnTq5eTg0UgOKT6du9DOlLq5Rq9XSSUnNIvNvX331lTu44N8nlKDQNGl3woQJbuy/eoIkcytFBZVqDa929GzVBMezzz5ro0ePdk+iAIpHjSSPPfZYu+eee7wr2SFv4Pjuu+8Ou6/HdTBBK67+7aSTTnKT2v37hBIUiupH5syZ407XJLN+RFs1y5Ytc7UpWhVhqyZYDhw44FbFXn75ZWvYsKF3FUBh6WfptNNOc+0MwjTrxg8c/qqGVjhiw4ZuseFCt6OPPvqw+4mclCSUICEKDdOnT3erJKofSebYf1Whq9iLrZpgGzhwoFtq1kkcAEUzd+5ct9KsgB8UOtHoBww/cPhBw7/mBw7/o1Y4YsOGbsloA0EoQYH0jakfIn3D9e/f34477jjvkeLRr6sTHSqU7dChg9WrV4+tmgBbs2aNtWnTxhW80n0SKBrVkmiuVOfOnb0rqRUbOPygEbvKoZv4AcMPHH7Q8K+lqu9UXoQSHJFG1yuQaMleWyrJ+MbUqosaoGkQVatWragbCRGdGLj++uvt2muv9a4ASJRWmtUwTb1JkhHs/cDhhw19Hhs4tNWimx8s/KARu8qRzsCRCEIJ8qXjuFrJ0FjtZNUR6IdyxowZVrVqVepGQmjx4sU2ZMgQN2wRQMHmPvecDfvv/7aNO3da1RIlrFOdOjZizRqzAk7dKHDEhg0/cMSeVPEDR+yqRmzg0FaLrocJoQRxacidGmbpCKgCRHHpB8vfqlFreOpGwoshfUBiVD8y8MorbdrevaZuJG/m3Lrl3Eb36GEXjBoVd4XDDx36GBs2/MARW0watsCRCEIJDrN//37Xf0Q/KDfffHOx60eU9pcsWeJO7Wibhq2a8NPxYPWQWbRokXcFgC+2hqPr5ZfbhI8+spY//ug9mhtMrilZ0rr84Q+HhQ5/hcMPHdkYOBJBKMEhaoim+hF170xG/Yi2anSqpnr16mzVZBEdadT3iDrtcjwYUaI3a7HbJ7r/zTffHLqvm/grGUPuusv2fP+9lTh40F33HV2ihH0XE1TwE0IJHM2VUYBQMzQVnxaHfjC1/aOtmu7du1udOnW8R5AtJk2aZK+88or95S9/8a4A4Ra7wqFbvMChVYzY7ZMTTjjhsO0V3WLfzDVq1MjG5HxNi7/9zbuSu1LSq0IFe3/79twLOAyhBK4Zmk7D6Liv3gEXlU7V6Oz90qVL3dHR1q1bs1WTpfzVEoUSHeUGgqywp1R0KyhwJEI1JTf8939b/5z/1x/277e3jj7auuX8GmMmTrTOXbt6X4VYhJII0/TdKVOmuNbuantcnPqR9957zxWyalVE7eGjuh8aJU888YRbEUtGEygF2fvuu8+d7GnWrJl3FShYfqdU/LDhf1So0POSHzTSdUqld+/eNnv2bPd7qFatmg0fPjxtPUrCiFASUdpaGT9+vPshURdV/VAWxZYtW9wLkwpke/ToYTVq1PAeQbbzV0uefPJJa9q0qXe1aP74xz+6VTWttt1xxx3eVeCn9ub+Le88Fb3Yx4aN2MCR6aLRffv2uZo6BXdWFBNDKIkgDbvT6Yni1I9olUWD8zS/Qb+OhvOxVRM9WmnT+IHXXnvNu1J4Gi+gjr4vvviiewepd5UlS5b0HkU28wOHv6IRu6Xir37E1nDoVpR5KpkyYsQI11pBReFIDKEkYrSqocZXaoh29tlne1cTFzs4TycvFEiKusqC7KC+JSNHjrRLLrnEu1I4+n70m7Lppv4n559/vvcowkqBwg8bfuDwg4Z/zQ8c/sfYLRV/9SNI3UYLY/fu3W4lUW/ctCKNxBBKIsLvP6IniT59+liFChW8RxKnrRqd0Dn++OPdlk8yh/IhvLSycfvtt7sn36LUJY0aNcoFXBVG60TP3//+d7vtttu8RxFERTmposDhBw3/WlgDRyJ0cEBbnI899ph3BYkglESAniBUP6InAXVoLewTgZ5wXnjhBdu0aZMLI3pnDMRq27at24LR91dh6OmnY8eOLiz7NBPkr3/9q5UoUcK7gnTK1EmVbLJ582a74IIL7P3337eyZct6V5EIQkmW8wfqaUm8sN1U/SO+6tzZokUL98JTunRp71HgJ/4EYT0J6wUpUW+++aY7Vjx69GjvirmTYNoW1PA/JF/s9okfOGK3WfzAEbuqka6TKtlCk4AbN27Mil8REEqy2PLly12BlVY39ANSGOrG+tRTT1mVKlXcC0RRtnsQLQoTn3zySaGK+saOHesaTMUeA9bxYG0F6ddD4eQNHHlPqujxvCsaChyx2ywEjuLRUXm9EVTxdzImAUcNoSQLaflVp2s+/fRTGzhwoFWqVMl7pGB64tJWjUZrs1WDwtDxxzPOOMPtoas+pCB66unZs6c7vRO7VaPr11xzjTtqzBbOT/zA4a9qZNtJlWygn4H69eu72rtzzz3Xu4rCIJRkGT0xKaWrGFVNe/QklQh/q0bD83RMWFs1HPFFYekUjU52qZkee+mJy1s4GrWTKtlCq3uff/65aySZEs89Z3bllWZ//rNZly7exexCKMkiWhkZN26cq/+47LLLEg4VegHRVo2a/HTr1o13UygWnTrQO0a9W8ThgcMPGrGrHLqJHzD8wOEHDf8agSPYVB+lWhJtPWrbOyVynp/tqKPUudByko93MbsQShKxYIHZH/6gQgszDZd74AGzli29B4NB9SPqQaLVkQYNGnhXj0xPhjNmzLCdO3e6rZratWt7jwBFp8Z6WsLWiS8VWGezwp5U8YNG7CoHgSP8dPRXW91Dhw61K7WSkQoKIiecoCduM9X47d6dG1CyDKGkIGvWmF16qdkzz5hdcIHZq69aziu4meZ9/J//431RZmmpUF1ab7rppoTqR/REOm/ePBdkNKeGbqxItgU5QV7bODr9VZyZSpmknxM/bOzYseNQ6FDoig0dsWFDn3NSJXq0baNjwCmdmv3Xv5o99VTu1s1ll5n93/9r1rGj92D2IJQURMtl6lR51VXehRxall682Ozpp70LmaE6EDVE05Pj4MGDE3rye+utt1x7+Fq1armW3jxhIlVUrKoW8uXLl3ct5Ldt22blypWz9u3bu3eUv/71r72vzAz93GgYpVYK/bCh8PHvf//b3VfDQYUK/Z5Vo6XAr4Cl+37o4OcH2rbp0qWL27Y59dRTvaspkPPzZBdemPtRr0F/+5vZk096D2YPQklBVKyX82RqsUe7ct4d5Xz3mX3zjXch/fTkqUCiLRf9QBS00qGvV92I3tl17drVtT8GUkmdXq+44gpXq6Rgohd0ff/pe1FbHDo6qdqnVND/JzZ06P+nj7EhxC8YVdjQ5zr2XrFixUPXFThYQcSR+KdttFWZyImzIst5A+pei3IC8yHHHpv7GpRl36OEkoLoSGK8v6L/+A+z77/37qSXeohMnjzZ9Q8paDqrnpznz5/v5tUwOA/pohMI55xzjpv5oW6feWk14oMPPnDvLgu7YqIVQj9gKFzEhg4FHn1UjYa/faJApJEICkUKGgohusbPAYpLRd1HHXWUCyUpNXeu2UMPmS1a5F3IoWGqv/td7lZOFiGUFETpNOeJzoUQX046doVGGVgp0btP1YLoh6Gg1Q5t1aj4VSOztVWjJ2ggHQYNGmR/+9vfjljjpEZrp59+es7zbc4Trkd1G/4qh266n3emigKHvpe1jaJfX0FDN610KIhoqyWsdSwID630PZQTFNQkLeXfb717m6loPPYYsI4H6xCGf8rto4/MNMjyiy9y74cUoaQgqiXRN4P28XzTp5stXJjWmhK9O9TqiJ6kNV/kSHvZW7dudVs1KtRTsSGD85Bu+p6rWrXqEZ+sFT401v3ee+89FDgUNvztE92YqYIg0lgF9XJ69dVXU39qUVs3egP64YeHb9Xoeo0ampRqNmaM2axZZm+/HX9lP0QIJQVZt87sootyK56VQl9/3eyKK8zmzTOrV8/7otRSEJk0aZJ7V6iju/ktO+tJXt1Y9QOjrZomTZqwRI208E+m6Kbvw9/85jcJ7bGr2do//vEPAgdCY/fu3W4u08iRI90wyUCYOtVy3oGalSxJKImEZcty9+42bDCrWze3T0nz5t6DqaXGZuolUtCAshUrVrhTNQoi7dq1Y6sGSRMbOHSLnaeix3SLXd3Q5zqeru3FglZK1q9f757kgbDQCom2xBVKAie/GsgQIZQEmIKGepBouya/GTRbtmxxdSMlcxKyVlHYqkFh+IHDr+OIbfwVL3DoFjtPxa/nyLvCUdSaEiDIRo0a5Xo8adtGBa6BQyhBKqh+RJNWtd+u/iPxJvT6WzV6p6lVlMJOAUb2U6Dww4YfOPyg4V/zA4f/MVnzVPzTNzVq1LBjdXQxj71799r7779fpNM3QCaoTm/YsGG2cuVK9/MRSIQSJJuOOWqgnk4WqEhVLxZ5KaVrq0bHe9WRtXTp0t4jiIrYeSq6KWjkPaWi753YVY50z1NRvUj37t3d/1ffzwonCklffvmlffbZZ3bhhRfaSy+95H01EFxatdZcsEWLFgV7HAehBMmkgXo6737++efHHainlt3aqtELjbZq4q2gIPwKO09Ft6CeUtGKyW233eamT/sdXS+44AIbPny4m9Ok7q733HOP99VA8Oh7WN+zGjCpYadILUJJQKxatcoFDq2O1NHQvxh6YdJWjepHtFXTsGFD7xGEUez2iR84YrdZ/MARu6qRjfNU/FMMt956q1177bXeVSA49D3apk0bu/76661Pnz7eVaQSoSQAVMyqLq0qaI0tDFRtycsvv+yGm7FVEw55A0fsSRXd9HjeFQ0FjthtlmwIHIny34XqJEPKpqsCRaAW8i1btrSLLrqI1bw0IpRkkN4Rq35Eg780ZTI2cGzYsMGtnOgFSnuZRzrFgPTwA4e/qlHYkyq6RSlwJErTVRVMNGH13HPP9a4CmXPgwAH3JlD1Iw+oBQTShlCSIV988YULJPqm14A8f/9f3Vh18kYvdCoSzLuVg9TIWziazpMqyO2QqReBxx57zC5WB2UgQ7RCom30MmXKuO/HQB79zWKEkgzQUV9/oF4rDVXKoXffc+bMcVXeKv7TyQS6sSZHbODwg0bsKodu4gcMP3D4QcO/RuBILX3vK5g8+eSTdskll3hXgfRRINHUdQUSbasTSNKPUJJmOsqrJ98BAwa4Hg6iAXsatFerVi23aqITCkhMYU+q+EEjdpWDwBEcOkasFwWddAhMC29EgrZs9L23Z88e9wZRwQTpRyhJE9WN6IlWL5z+QD1t4aiFvMa464hvoM+/Z4gfNPxbVE+qRMnSpUvdi4OKXznxgHTQCsk111zjTtsQSDKLUJIGevEcN26cCx0KH3p3ryLWt956yy1XR3WrJjZwKFzk3VLR437Q8G9RPqkSJaox0VFM9e3hVA5SSYGkU6dOduqpp9rEiRMJJBlGKEkx1Y9MmTLF1Y/oeJm6sSqJZ/tWjR84/FUNP3Douv9YbLjQ53m3VAgc0bZu3Tr3YqGtzhtuuIH9fSSdVkY0YE9vGClqDQZCSQotXLjQtdFWJbeO9Gr7Rqk87Fs1xTmpoqDhr35Qx4GCqI+JVkx0VJgXDSSTvrcUenXaa+jQoXxvBQShJAXU9Gz69OmuIdrAgQPtlVdesdWrV4diq0bBIrZmQ/fzzlQRhQr/psARGzYIHEgmvZvVz46W13Uyh+V1FJdW4fQ99bvf/c4NPUVwEEqSbMeOHW5fUi/MZ511VqBO1fgrGbFbKnlXOMQPFn7QyLutQuBAuulkRP/+/d2LibY/9X0IFMWzzz5rN954o3ue5oRX8BBKCkHLfWPvvNNmz51rn+zcaaeWLWsdO3Wym++4w41f12yaBx980M3z+Oijj9wTp2pJ0jE4LzZYxBaNxoYOybui4QcOf5tFjwFBNWLECHv00Udd91dmQKGwJk2aZEOGDHHBlu7BwUQoSdDi+fOt1xVXWO/vvrPOP/5odXOubc65vXD88TahTBkb+Pvfu26s1apVc9sdWhlJVt2IQoZWYBQstm/fftg8FT90qM4jNmz4gSO2mJTAgWyg4ZTaFuWdLhKlWr7rrrvOnerSFmC9evW8RxA0hJIEaIXkvFq1bGZOGGjqXYu1+qijrFWpUnZ5t26uv0Jh6kbUqEehQ2FDIUPhQ9cUNPxrqlE57rjjXLCoWLEiJ1UQearX0s+aRslrNglFisjPtm3bXP2I3jD6W+sILkJJAm687DI7cc4cO9KcyLuPP97Wt2ljL774oncl/26jChsKHvqopmoKHAob+mHxw4f/efny5d3ntJwHDqcCWL371ZsGvfvVFioQy19VU0Hrbbfd5l1FkBFKElA9J3DMyQkR2rLJj7Zy/uuEE2zYiBEubGj1Q0Hk+Jz/NjZkxIYN1ZroI4EDKLr777/f7rvvPmbm4BAVRqv+aOrUqa4VQ+vWrb1HEHSEkgSUKFHCEvlLKpFz05OjwsYpp5ziAkfZsmXdaRVtr8R+BJA8q1atcv2AVLw4ZswY93OHaFLdiL4X9AZQQVVHyREehJIEJLpScm7OE+HsOXPcNo22Z7Q14xehxn5UKFFdiFZM1HPB/6jAor1xfdQKi67r63TT/dKlS+f+zwD8jLZztFSvoX5qtMaqSbT4qyNjx451zdDUBZieNuFDKElAIjUloypWtLUtW7px1wXR1o5uCi6qCvc/+sFFp3c0pE/X/a/VfYUcBRaFlNiVF92OPvron13zvw6IkgULFrieJn4RLKsm2U8rZfo315s6bdcw3DS8CCUJ8E/f/OW77yxeZ4SNpUtbmxNOsFffeCPlxXYKLn69ir/yopuOCee95n9dvKCiayfk/J79z2Mf868BYaVAf8stt9jcuXPdqolaiSP75F0dUXdWTmKFG6EkQYf6lOzda5pZqhyuLZvZxx9vD5UpYxMffzywy8Xxgop/Tasy/uf+Y/7j8YKKPsZblfE/J8wgSLSVoxM6qjXRxGHVGSA7qHbkmmuucdvcrI5kD0JJIWjFZMigQbZ02bJDHV1b/OY3Nnz06Kw8jhgvqOhjvFUZ/3PJG1L84OLXy8TbfiLMIFW0NXr77be79uJ6N33ttddSaxBiqh1S5+wJEybY8OHDrU+fPqyOZBFCCZLKDyd5P/qfa2Um3vaTPo8XWPQxv20m/z6QCL2zVjj55JNPXK0JWzrhoq2aKVOmuDbx6uR75513uoZoyC6EEgSGwknewOJ/jLfN5N/PL7AozPjX430NoklDMocNG+aW/XV8mBkowafaINUIValSxa2O8G+WvQglCL3YgJI3sOjdlT7G+5r8AktsmIn3NfqI8NO77tHe1uvIkSOZhxJAS5cudQFSW3BaGeGYd/YjlCCy/JASL7D4YSbe10jewJI3zPjXYr8OwaN/5yeeeMK98Ond96233sr04QDQsW41olTPJ61maauNupFoIJQAheSHk9jAkjfMxF7zvy5eUNEtbwFw7OP6iNTz6xX8lZObb76ZmpM007+BipEfeughd6RbAfHqq68mjEQMoQRIk3hBxf88tgA49nHJG1TircrEPqaPKBq9MGqIm96lq+bk+uuvtyuvvJLTOimk1ZCnnnrKHn30Ufd3rm0aBUL+zqOJUAIEWN7woo/xVmXyPha70pI3uNBnJjHaQtC2zubNm9079quuuoqtnSRasWKFG5inEKiBef7WGSsj0UYoAbKQH1LihRr6zBSOjhLrxVNbCzr94a+e0L6+8NTrSasiTz/9tOs3op4xPXv2zMo+TygaQgmAQ/KGmbzBJcp9ZvytHb2gqlOsemX07t3bzdjh3X3+9PemVScFO/29aWvG/3tjiwZ5EUoAJIXCSd7A4n/Mtj4zesevUzsKKPpcAUXbO7zQ5tIRXh3nnT59uusxopUQ/f1oZYRW/zgSQgmAjIoNKHkDSyJ1M7FBxQ8zea/5X6fPk00dYrW189xzz7n6k6ZNm9pvf/tb11Pj1FNP9b4q+6lgVStJ8+bNc4FE3Va1IqLARudVJIpQAiCU/JASG1T8a/ltM0m8oKKPfgFw7LXCrspo1UQvyAoo+qi6E4WTVq1aubBSnJCiFYdhd91lG3OCT7Xq1d0cn86dO3uPpp9CiIpVlyxZ4rZn9GfX1kyHDh3cxygFMiQPoQRAZPgBJTao+J/7BcCx1/xgEy+o6H5B9TIqktUL9iuvvGKrVq1yR171gn3OOee4DrK66VpB5r7wgg289lqbtm+ftTh40N5s1Mi6bdtmY8aNS0sw0XbMunXr3J/n3XffdX8mhZK6deta+/bt3Z9JfxZqa1BchBIAKEC8oOLfP1K9jB9O/KAiX375pX311Ve2fft2++KLL6xSpUpWo0YN+9WvfuVqL6pXr+7G8Me+wDc65RQbkxMCWnj35c2cMNBryxZ7//33vSvJoS0orXpoW2r9+vUujOimVR8FjzPPPNMd4VUgoX4GyUYoAYAU8cNJbFDxg4tfL6NgouOx/teUKFHCDh486D7/xS9+4e7Pe/pp2+X9mr7/LVnSyuTcXn/9dRdsKlSocCj4+LTCoRUN/b/UJVWfb9u27dB1BaONGze6/7+u6+aHDwWjs88++9DnrIIgHQglABAwCiRaqfjggw9cUJh4/fU29scfD1speTUnJHQ4+mhr27at6WncX7XQNpRCjT76T+9+wCldurQdf/zx7msVPsqXL2+nn366CzRapVEfFiCTCCUAEHBzr73WBk6fbtNyPlcweTPn1q1cORszefJhNSX+akzej/7nUe4zg3AglABACMwdMMCGTZtm6/bts2onnWTDH3nEOnft6j1afAoneQOL/7GgPjN5g4pu8cYZ+F8H5IdQAgAosnhBRbd44wz8r4sNKrErMPmtyvjXkP0IJQCAtIoNKnlXYOKtyvhfFxtUYoNNfnOZ/I8ID0IJACAUYoNK3mATr17G/xgbUGKDC/UywUMoAQBktdiAkje4FKbPjB9cFGbye0wfUXSEEgAA4vDDSWxQ8YNLInOZ4gWXeAXAsV8fdYQSAACSyA8p8UJNvAJg/3PJG1L84OLXzajHjD5qVUYjCtR3Rv1nsgWhBACAAMgbZvIGF201qRuv7qsj7/79+93noqCicKKPJ598sgsv2mZSeImtlVHDPP/rgohQAgBAiO3atcuFlp07d7otJH8byQ8tuq8xA3640df9+OOPVq5cuUMrL1p10ee65ocWP9CkM8gQSgAAiBh/FSZviFFg0ce8IcYPOPG2lvzP89bL5P2aRBBKAABAQvww43+M/TxvvUzer1E4id1K8gNLbJ8ZQgkAAEg5hRN/VSZvYPH7zBBKAABAIPzC+wgAAJBRhBIAABAIhBIAABAIhBIAABAIhBIAABAInL4BgGxVooT3SRxHeuov6n8HFBOhBACiQEGjKE/3Rf3vgCJg+wYAAAQCoQQAokgrIPFuQAaxfQMAUaDAwfYNAo6VEgAAEAiEEgCIotgtm9gbkEGEEgCIIm3JxLsl6qOPzCpV8u4AyUEoAQAUzujRZt26mW3b5l0AkoNQAgBRUJhVkFjx/ruTTzZbudK7AyQPp28AAEWjGhReQpBErJQAAIBAIJQAAIBAIJQAAIBAIJQAAIqGehIkGaEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEAqEEAAAEgNn/B5EkP1DQcIBlAAAAAElFTkSuQmCC" width="400" /> </div>
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<b>La inversión puede ser positiva, si K>0, o negativa, si K<0</b>. Si la potencia de inversión es positiva, un punto y su transformado se encuentran al mismo lado respecto del centro de inversión. Si la potencia es negativa el centro de inversión se encuentra entre cada punto y su transformado. <br />
<br />
El punto de tangencia (T) desde el centro de inversión (O) a la circunferencia (c) coincide con su inverso (T1). Como no podía ser de otra manera también se cumple que OT*OT1 = OT*OT= K, por tanto, OT = Raíz cuadrada de K. </div>
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Todos los puntos situados a la misma distancia del centro de inversión que este punto T forman parte de un lugar geométrico denominado <b>circunferencia de autoinversión</b>. Esto se debe a que la circunferencia transformada de la circunferencia de autoinversión es ella misma. En el caso de potencia positiva los puntos pertenecientes a la circunferencia de autoinversión son dobles puesto que cada punto y su transformado coinciden. Cuando la potencia es negativa los puntos pertenecientes a la circunferencia de autoinversión tienen su transformado en dicha circunferencia pero en el diámetro opuesto. Por ello <b>se puede decir que la circunferencia de autoinversión es siempre doble, tanto en potencia positiva como negativa, pero sólo se puede hablar de circunferencia de puntos dobles en el caso de potencia positiva. </b></div>
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<img alt="" height="523" 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rIqbZeLVxA8EA2ZH1JrbPR3rgIAXE8DUzXxfN48s9On3UmkgUp1dNecfo7o09TxVatW2YYNG7yBgLgRwQO1peXipUvNmpvNRkfdSQBAXpr7oeGpGqKKxHv66ae9C1n6OaJNXx9NHe/u7vbCBwojeKB2NABQU3sVPKhXBYDinD1rNneuWWcnz50JpV2PNm3a5F3M0s8RXUFZ1SOPPOJNH6esamoED9RG5snUu2tHTwcATJ/mfXR1+avFuomDxFCJzooVK7x5D/RzRJdWNrS7WH9/P2VV00DwQPUtWGDW1ubftQMAlO7gQT98aHMOxJ76OFSuc+jQIXcGUaOQoR4O9d1QVjV9BA9U38mTTOcFgEqJyvPpTZlLikIP+c53zN75TrNbbzV717t0le2fn0y+jxU8pJSPGVHPPPOMdzF76tQpdwZREpRVaQigvlasRpXG/eQCAABUSBAMst19t9m3v+2//cUvmv3rf+2/XawwPmYE6AJ2x44dXhO5ZnUgeo4cOeKVv6msiq9ReQgeAACgsvKFhGy6W6xViukI42PW2MWLF72hgAoeNCZHj3arUlmVejm0rTHKR/AAAACVNVVI+Kd/8kukRO+b75Er37ls2R8zBk6cOOGV7Rw4cMCdQVRoFUrlVPr67Nu3j7KqCpripxgo0Z497g0AQM309vp9ddU2VUh44gmzr33NHRQpjI9ZI7qYVRM5/RzRc/jwYe9rs3XrVsqqQkDwQGWpyVF7y2s+B7usAEBtbdli1tBQ/a3LJwsJCkJ/+qfuYBrC+JhVRj9HdJ07dy6TXZ+wnp4ebzUK4SB4oHIuXPCHWi1ezFArAIiKiQmzxkZ/flK1FAoJ//iPZp/85PU7cel98z1y5Tsn+T5mBKmHQ/0C27Zto58jQjSscWhoyCurOnjwIGVVISvwUwxMkwZYaS95LesDAKIluDGkOUrVuDGULyRo96kPfcjs6lV3YppK+Zg/+IE/rLbGdAdd5Tt79+51ZxAFChoKHFqFUgBB+AgeKN/QEFPIASDqtCKgaecqhT192p0MSb6Q8Gu/5p/PfkzHdD+mej7uvTf/n6siNY8rdFC+Ex3qrdFuYiqtUokVqqe2P42IN72IZZ5MranJX8oHAESfSq7q681GRtyJhNq61d9it0bBQyU7AwMDXj+Hpl2nSnYQDIY7fve77jdrR301ahrXoEY1kaP6CB4o3dmz4fVzZD9pBU9c03mRLPfPA0CSDQ/7JbJpoNeAKlPZju6ob968OZ39HNmfc4W/bdvM3vY2d6L6FAK1k9iyZcts9+7d9NjUUPV/GoFi5L5QKDTcdlvx4aHcPw8ASIYqBw8NBdQqhy50Uyvf51yvwTWgwX8aAKjG/tStPEUQwQPXOXv2rHV1dVljY2PmeeMmm3XnnbZkyRI7We194PM9aSk0FDuVttw/DwBIhioGj2AGxNGjR92ZlMr9nH/pS5a58ncH1aEA2N/f75VVPffcc+4sao3ggWv27NljDb/yK7Z67lybeMMbvCeOk5lH7y//sjW8+c02rKX5ain0QhGc16/5HoHst7MVOg8ASKYqPO+rlOepp56yNWvW2Pnz593ZFAtek7MfVdrOWV+LYOq4fmV73GjJfCcA/kqHQsdBbYmb5wljPPNoyISRqq186O/Np9D5XOX+eQAAinDlyhVvd6S+zIX1Sy+95M6mXO5r7fe+Z3bnne4gPFrZ0AqHVjoY0BhNXIXBo/Kq1f/qX/lPFgUeva96lS1873vdnwiZ/s58Cp3PVe6fB4C0Wr1aS+DuAJPRVqy60N21axd31rPle619zWvcG5Wn3g31cKiXQz0diC6uwuBp/LVfswk9KejJosBDZVezbr/d/YmQ6e/Mld2jkfXvuu4RyH47QI8HAExNoWPmTGYzTUEXuCrnSX0/Rz65r8GbN5vNm+cOnAoMdwymji9dutRr5if8RV+eqzOkkRrJr128T/Lw3q8acv+er3/d3xFDvxaj2D8fkam2ABAp2mpX4aO/351Atmeffda7u65BdMjDXTN4D93wU+j44Q/db2ZUYLijGvmZOh4/pX/FkSiNd91lE9lPFHke3opHiEul18n5u70nrulshVvMn4/IVFsAiCSVrDQ2+oNiNTAWXg+HZnOop0O9HShRGcMdVd6mz39PTw9Tx2OIKy54uj79aVs9Y8YrF+p5Hr2Zx8J77nF/IgFqPNUWACLvwgWzuXPNOjtTHz4uXbrkXezqDjslPRUyjddfrWroc69VjoMHD/I1iCmuuODxdrW64w4bcyEj93E882h41avs5He/6/5Eguj/CADI7+pVv1QmxeHjyJEjXhO5yntQQUW8/ipgqH9DfRzq56CsKt644sI1e379163hNa+x1S5o6AlB5VXrM4+Gm2+24aYm/wUoafR/BQAUprKi+fP98quUGRkZ8YYCsltSCKZ4/VUPDVPHk4UrLrzi8mVv5aPzPe+xxttvzzwf3GSzbr3VFr7tbXby4EGzjg6ztjb/BShJCB4AgBy6075t2zaGAoapwOuvZnBs3bqVqeMJxBUXihcsty9alKzldoIHACCLLnyDfo4XX3zRnUXYFPY0bXzZsmW2e/duPvcJxBUXpufyZb/RcPlydwIAgOQ4ceKE18CsvgJUj0rZVFalCfCUVSUXwQPTp/DR3Mz+7gCARDl06JAXOqrRz6HteE+fPm2jo6Pe3f3169d7vSSdnZ22aNEia2trs9mzZ1tjY6P3qKur80qgcx8zZsy49j7NmdfmefPm2cKFC72Po4/X29vrffz9+/fbyZMnI7cN8MWLFzOXE/3ev5WyquQjeKA0ExP+cKmhIXcCAJBaCSi/3bVrl9fPUenZELqw3rNnjxcsFAYUKBQQFCQaGhqspaXF2tvbr4WELVu22MDAgPdnJjKvtQonehQKDFevXr32Pnp/BYzBwUHbvn279/H0cfXxW1tbvXASBJUgoOh9hoeHvR7PagrKqrRblT73lFWlA8EjbTJPLhUrkxoft8yzptnoqDsBAEgd3YDSxiMx3fVQ8znWrl3rDQYsd6tWhYxgF6z58+fbrFmzrL6+3rvo1wX2xo0bvd9XQFBgqBWt6CigKOR0dXV5YWjmzJnev1WBRP9WrZJc0ByXEGhlQ43jmzZtoqwqZQgeaZJ5EvFKpCq5hKwgk3lirejHBADES+ZCO47hQ6sbCgmaD1HKQDoFDV2gL1my5Fo51Ny5c2316tXeKoJWIV6O0WqQgoaCkVZBFED0/1F40v9Pn6NyV0X0+VLYUDkbM1HSieCRFgMDfmmUSqQqTXe79LEzT7AAgJTSarpmfcQkfOjCVxfAGg44HWNjY96F+Zw5c64FDe2ApfO1XMUIy/j4uFcmFgQR/b8VrNSbkhuqFLZa7rnH6l7zGpudCWJDO3d651VGpYCmlZSnnnqKsqoUI3ikwciIHwwyT4qh6esz04DBixfdCQBA6ixZYrZgQeTDh+7ea6VDKxJTUZg4ePCgd9GsciT1ZejPqgcjiUFjKirRWp4JmVrh0edDpVo6pz6Nxje+0fa/+tWZq8ubbDTzaLztNuv93Oe8z5dWOlTWhnQjeCRdEDoyT5Ch090ubbWbwidiAICzeLE/cDaCJUYvvfSSt4PSE088MeXuTlrBUImRSo3UAL5y5UqvNwOvUK+IVj+0CnJ7JnDsu/lmL3QED4WPu26/3Y4ePer+BNKO4JFkWuFQ83eYKx25NFxQd7uSNGAQAFA8Pf+3t/uPCL0WnDlzxtu1ShOxC/VzqAdBZUW6kNZDJVTV2FpXfvCDH9g73vEOe/3rX++VJcXN62bMuC50BI8ZWgEBHIJHkrW0+Cse1aTVDr3YaLkdAJBOwWtBRDYe0S5KjzzyiO3du/eG0KE+BV3od3R0eGVUKh2qxcrG7//+79sXv/hF+/73v29vectb3Nn4aGlutv05oUMrHr+SCSQqVQOE4JFktbrTpOVrhZ7eXncCAIDaCLa3ze3nuHz5slcmpF4FbX2r8FHLno077rjDC0FxpM/tRz/6Ubvr1luvhQ+vx+OWW2zZ4sVeqZqGIWo1KWoDDFFdBA+EQ9PN1Wyu3bQAAKiyoJ9j1apV113sastYNYqrd0MTwtXLEQWaQh43mnuyc+dO7/OpYYAKby2ZIKfyquY3vcmG/vN/du+pVtM9XsBTQ7qCoMrakD4ED4RHd5fUYzI46E4AABA+BQ01kGcPBVSvhoJGsCtVWMPxShW3FQ+VTy1btszbHnc6qxgnT570vg4aVrh48eKqT0xHbRE8EK7ME4w3YHD/fncCAIDwaAclBYugn0OBo7Oz0yupUrO4Sqyi6EMf+pB96UtfsmPHjkW6x+PEiRPe51GN+qdOnXJnp0+BQ/00rICkC8ED4dNWvkw3BwCETOU+KvvRUEBd2OrOukqqdKEc9d4C7Wr1tre9zbsQV19K1GjlaGBg4LpQVwkKHNqqOAgg9IAkG8EjCbZvj/7sDD2JNjYy3RwA0i4TAqzCu0bpIlgXxern0B354E66Bt1FdYUjLvS5PXDggFdWpcGLYU0dV+mbgqK+bmpCj2ujPSZH8Ii7zA9nbIb29ff74YPlVABIr8zFq9f/V6EeixdeeMHWrl1rn//85+2v/uqvvAtXlVZFrYcjjhTiFObUL3Pu3Dl3Nlzayri1tdWam5tjOc8EkyN4xJlWOrRzVJwu5HWnq62N6eYAkGbd3WZz5vg7IJZBQwF1J/4LX/iC3XfffTZv3jwbHx93v4tSqfxJjfmPPfaYHTp0qGJlVdOhXbDUl7Nw4UIa0BOE4BFXQemSmrfjRsMFFy1iujkApJleB3QjqkQaCqjQodUN7VS1ceNGynPKpIChPhkNW3z66adDK6sqlvo91LNTV1fnzVyp5ZwVVAbBI45UGztzpvaycydiaMECy7xauAMAQOooJMyb5weQaVKvwac+9SlvKJ0uTGlILp9209JOVZs2bYrcDlPamUxDCOfMmVOTqfKoHIJH3Kg5Wysdw8PuREzprkVrq9nq1e4EACB1VGrV3Gy2cqU7MTntrPS5z33OPvaxj9nb3/52289W7WVTyNi6dasXOnSBH1Vazert7fVWP7RLGatb8UTwiBPdgVBPR1Iu1vWk0dLi96oAANJJJcP19WYDA+5Efmoif/TRR+13fud3WOWogKCsSp/LXbt2eZPe40DhaO7cudbW1kbvRwwRPOJET85dXcnqjdCThu52Md0cANJLpcOjo+7gRt/73vfsoYcest/+7d/2mo5RHvXHqHG8v78/cmVVxdBqh7bc1YwWbaOM+CB4oPaC8jGWzAEg1YaHh63lbW+zul/6JZvd0GBDO3faV7/6VXvggQeso6MjlhfJUXL+/Hl78sknvVKlcqaOR4VWP5qamry5LTSexwPBA9Gg7Q+1rzvbIAJAKil0NL7udbb/psylSeYxmnk0vPrV9v+1tNhf/uVfUtNfBvXGaCaGdgFTeVUttscNiwZEavCgGs8pvYo+ggeiQ1sEV3CoFAAgPlrULO5CR/BQ+Ph19X+gZEePHvX6OFRWdenSJXc2edR4ruGRo5OU7KH2CB6Ilr6+igyVAgDES/1rX3td6AgeM179avcemI7nn3/em+ielLKqYqj/RzNd2PUquggeiB410M+dq8lB7gQAIOlafuM3bN+rXnVd6NCKR/Odd7r3QDE09G/Hjh3eEMB9+/YlqqyqGCq3am5u9gZL0vcRPQSPqNIuDWn+gdGAQT0IHwCQeLo4fvDBB+3OW2+9rsej8ZZbbEgr4SjKgQMHvC2HNZcjyWVVU9FWy9qMQFvuqgcE0UHwiCLNtZg9O93lRgpd7e1mixcna/tgAMB11PisXYl0kbhq1SpvV6sZmcDRfNddNvTxj/vDZjEplVI98cQTXmnVae0UCY++r9R0zuckOggeUaNdnWbNMpuYcCdSTOFDJVcqvQIAJI4umD/xiU/Yb/3Wb9n/+B//w53N0dFhtmSJO0A23dlXWVV3d7cdPnw4dWVVxejr67PGxsbMZRXXVVFA8IgSrXAodAwPuxPwdrjStPYtW9wJAEAS6EJZ5VWaRD7pfA7dhGLQ7A3Uv6E+DgUPprhPTkMGtePV2NiYO4NaIXhECXd18tMSqbbZ3b3bnQAAxNmuXbu80HHfffcVV4Ovu9XMevIcO3bM1qxZ45VWnTlzxp3FVEZGRrxJ50y+ry2CR1SsXu1vI0s/Q3560Zk5k+nmABBj6udYv369feQjH7HW1tbpTSLfuNHvf0zpxivaHldN44899pgdOXKEsqoSKHTU19d7IQS1QfCIAv0ANDb6d/ZRmO5SqBSNpVIAiJ1z587Z8uXL7cMf/rD9+3//7zP5oYQAoaqAzk53kA4vvfSS7d271x5++GGvZEjb5aJ0Ch0KH5qUj+ojeERBW5sfPjA1PVFouZ2QBgCxofKgZcuW2QMPPODtXlXyfAWVZek1U/1/KXD8+HFvhWPDhg1ecENlBCsfTDmvPoJHFFBeNT3a010rRNNZogcA1ITuMP/Zn/2Zt3vV/PnzSw8dKfLCCy9Yf3+/t1vVc889586ikoKeD8JHdRE8EE9abldPDIOBACCS1IPw1FNPebM5PvrRj5a30pES+pw988wz3urQ7t27KasKWVB2Nc6mBVVD8EB8qc5XS+4AgEhR07gCh5qhH3/8cW+I27QayVNIKxsqq9JKhxrJUR3qm9HKB0MGq4PggfhSiZqChwII5WoAEAm6gFuxYoV3N3n79u3W1NRE6JiEPjcKGwpo6ulA9WnIoMJxUVs7oywED8Sbhia1tJgtX+5OAABq5dChQ15fgi6gtWuQJkZzJzk/7ValcqpHH33UK69ie9za6urqohywCggeiD/dodBU2/5+dwIAUE26aN65c6c32O7SpUtezbzKV6o2KTpmq96a2q6yKpWiqZEc0bBgwQLv8TJVFKEheFST7vqoNIhv6Mo7e9asqclsaMidAABUw5UrV2zt2rXeRbSaoc9mno8VOnQ3v2pUcjsw4A6iS1viauJ4T0+PnThxwp1FVGi1QyVXqzXUGaEgeFRL0I/AN3N4FOwUPpiJAgBVcf78ea+fY9++fd6xLtzmzp1b/Qs39UbU1ZmdPOlORIsmtg8NDXllVQcPHqSsKsIUnBsaGrweJVQewaNa1q/3exGoHQyXXnw044Pp5gAQKpUL5c6Z6Ozs9B41KVXp7bVM6nEH0aGgocCxY8cOL4Ag+oJSQZr9K4/gUQ26A6M7MXwDV8f+/X74iOidLwCIO5VRaaVDKx4B7QzU3Nxcu+ZchR0FD93oi4BTp055JWgqrWLqePzo+3n27NleKSEqh+BRDfPmmW3c6A5QFVoi1YBBtnAEgIrRHfsNGzZ4F9PZTdHBHeKa72ClG3z19foHuRPVp8+RVjfUPK5VIcTXokWLvBU8VA7BI2wKHDSU18aWLf7dL8rbAKBsmjehXat27dp1XY+CZh8odGhmRyRoxUPP/VV+3dXnRL0uS5cu9fo5mDoef/reVr+HhgyiMggeYZqYMJs5kxKrWurpIfgBQJnUx6E+hXzb4+qu8JIlS9xRRLS2VrXSQL0AGgCo1SCmjifL6OioF6zVdI7yETzCpIvewUF3gJrp6mK6OQCUSLv76KI6X5/CxszFfU37OgpRj18VwlAwdVxlVdlN9kiW9evXW0tLS/S+z2OI4IF06OhgujkATIMma6tXYdWqVXkbbE9mLu7r6uq8O8Jpo7IqTRtn6ng6aJc2BQ/me5SP4IF00IumtjPWdosAgEmpcVz9HMFQwHza2tpseQpv6GhlQyscWulg6nh6qJxuxowZNqEyepSM4IH0uHzZ3+lKTecAgLx0gaU7+SqxKnQnPyixStNWo+rdUA+Hys6Y75BOvb293mTzmsypSQiCB9LlwgWzhgZNdHInAAAB7cqk0HHixAl35kbaMnfmzJmpKbEKpo5rtyp9fiirSi8FjppM5k8QggfSR8uks2Yx3RwAHPVzqKxKQwHVMD2ZefPmpabESnM4mDqObFrtqq+vr/3MmpgieCCdFDo03ZxaTQAppz4FDQRUz8JUsye2bNkSzV2sKkw7eOlz0tPTw9Rx3ECrXwsXLnRHmA6CR6WodGdoyB0gFrTVcVOT6gbcCQBIlzNnztiyZcts9+7dU5YQaSUk1iVWw8OWSVfuID8Fr507d3qrHAczr+uUVSEf9TY1NjZ6PzeYHoJHJejOj5qW+QaMH03anT1br6juBACkgy6sdef26NGj7szk9L5dmosUV5rtUV9fcKVbZVXd3d2UVaEoe/bs8Vb/aDSfHoJHJWg6anu7O0DsrFzpb7Wbot1ZAKSbmqXVz1FsGdH4+Li32hH76c1a8Zg3zx34grKqtWvXUrePaWltbfWGC6J4BI9y6U65ynXYWi/edBdv/nx/9QoAEkr9HOvWrfMutKezFW57e7u3hW7s6e60VrkHB6+VVWklh7IqlEIzPWbNmpWqbaXLRfAo15IlZt3d7gCxpRcjBQ81i7FsCiCBzp8/75USabVjOhfZ+/fvt6amJrusWUhJkAkZh++91x7t6rKBgQHKqlCWzs5O7+cKxSF4lEMNdurt4EI1GYLwsXSpOwEAyaD+heDO/nRp+1yFlSS4tltV5mLx3Kc/7c4Cpbtw4YK36jHVNtTwETzK0dqqW0HuAImgO3oqnevrcydQNt1N/NKX3AGAatPOO9qlqZT+BTXQamBa3BtodVG4efNm7/OgEPbzf/gHs5kz/YZzoEwaKMiqR3EIHqXassUvy0HyaLq5ZnxoxyuU74tfZF4KUAMaCtjX1+fd4VdvRylmz54d6y1DVVL2zDPP2COPPOL1c1xXVqUbTB0d7gAoXbDVNJsTTI3gUSrdGWdZLbn05KHp5nv2uBM1MDJids89ZrfeavbOd5rt2+d+I+OmzI9uoUfg9tvdG1nK/ZilWLzYvZGR72Nt3uzvLAagYtTP8fjjj3vTyBVASjE4OGgtLS2xXe147rnnvJ271Eyvz8cN9P9KSt8Kak5bTavfA5Mr84oCSLDxcX/loxY7lunvbmgw+/a3/WMFhLvuMvv+9/3jbLkX8+99r9myZX4ZgX793d/1z5fzMUt1+LBlrnzcQUbux1XoeOghdwCgEo5nnrPUz7Ev+8ZCCebMmRPL1Q7dfd60aRNDAFFV2mq6vr7e6/lAYQQPYDJ60VX4qHYdsMr4vvIVd+Bs22b2kY+4gyy5F/Pa1u+P/9hfsfnkJ81+8hP/fDkfs1QKPv/8z+4gI/vjKnS8733uAEAlBP0cx44dc2dKMzw8HLvhaJOWVQFVwA5XUyN4AFNRP0/mBbiqpXWvf/2NM0X0InrHHe4gS25I+NGPzN79bv/XuXPNfvhD/3w5H1PH+R6TUQD6zGfcgRP8Ga2CaIgXc1OAilA5lZqnVVpUid11NBhti577YiIoq9qwYYOdOXPGnQWq6+TJk8z1mMIUVw4APD09/tbJ1XoyKXRRr96MXFMFgEAYHzNbbjmDho3lNpXr4yp0aPXlr//anQRQDgUN9XP09/d7Q/HKNTY2Zg0NDbGY2xGUVSl0HD161J0Famf+/PlMM59ECVcXQEppvkdbW3Xmtmh1IrtESbQ6UMzqRCFhfExR4NDKxtvedn0wy9e7oY8bnP/TPzX77nf9twGURP0cy5Yt80qsKtXLsGjRoshfOClg6f+sXhaVV5XaQA9Umrag1m5wcd+COiwEj2LxDQTJvCBXZcCg+i6+/GV34GgWRjn9GOV8TB3newRU1qWtKT/7Wf/40KHrm8oD+jPBz5Iukj7wAbMf/9g/BjAtah5/+OGHK3qnXw2yM2bMqEi5Vlg0h0N19Cqr0kDAimKXK1SAdoPTxH/cKOvKAQXprnC1a/wRTbpobm/XtCB3IiQqUdKOU9/5jn+sX3WsnalyZQeAyYTxMbNpNeXtb/dXPXKbygO5H1eB5fd+78YyLQAF6e6+tslVeVGlL7x7enpsYURnVD3//PPeXBL9v9XTUXF6fq/FZiJInO3bt3srh7gRwaMYqlXXxSYgurDWdPP+fnciJN/6lj9rQz0Y73qXf5zPdEJCGB8zm1Y9/uRPzB591J3Ike/j7tzp774FYEoaBLhmzRpvKGAYDayNmQtvlYpEicqqdu3a5e3WtXfv3oqVlOWlfj5mMaBM+tlUk3mUVw5rheAxFa12aPbB2Jg7AWRowKC+LwYG3Al4dMdQqyhMKgcqLujnGBoaCuXiW6UhTU1NmR/j6JQWHzp0yAscO3bsCCVo3UD/d1U4sOqBMi1ZssTb8AHXI3hMhdUOFKKLa83K0DRwvIItcoGK0yA8zafQr4W0tbVde2hnHV34/K//9b/c705NMwhWh11GWqTTp0/b2rVrvd26yp1JMm3bt5t1dLgDoDSjo6M2V1va4zoEj8lo+qSmP7PagUJ0EVBfX5vp5gBSQXf7tdKhi/HJKHAEfvGLX9g3vvENe/DBB92ZyakkRE3lU/0dYdPQv+D/q+b5mkwdD3o9aA5GmTSEczxfH2WKETwmo+mT1djBCPGmFQ/1fNT4BRtAsqifY926dV4/h96eSnbwCNx///3urcmpabu9xqv7ChraHlelZDWfOq5qBw05BcrQ29vrfU/jFQSPQoLVjrNn3QlgEur1mD2bnc8AVMT58+e9LWO1e1WxMypyg8ezzz7rXcQXQ9t/ai5GLZw6dcorq1LAqvj2uKXSqoeGxrLqgTJMTExkLiVn2lVKkK8heBSyfDmrHZge1UZnXry9Xa8AoETaKlbzObQCMB1Bf0f2Q7tBTeXChQtemVW1L460iqNg9dhjj3mzOSJnyxZ6PVC2OZkAy0yPVxA8CtGda616ANOhbRgzL/aEDwCl0BRu7eJUSkO1gka2EydO2IIFC9xRYRs3bsxcX1fvAlt9G/p/BmVV2i43krTqwUBBlEkbNnR1dbkjEDyAStILleqklyxxJwBgaiqnevLJJ4vu58gnN3jIe9/7XvdWYSqzGh4edkfh0mqOVjg0dVwDAYGk0zbYKreK0jbVtUTwACpNTy6trf4gKgCYgvo5tG3sdPo58skNHlpV+MxnPuOO8gvKrMKekaFdszTTQH0roUwdByJMgzm1vS4IHkA4tDyvxkTVCANAAboI19axk83nKFbQ16GH5ngodPzjP/6j+938BgcHvfcNi4KUmtZVVqVfI1tWBYRo+fLlkZmRU2sEDyAs6hHSXvBF7ioDIF20IqGhgLVsrFYPiLbSDYP+Xyqr0koHZVVIMzWXq8kcBA8gXCdP+tsyM90cgKO7/ps2bfLKq1RmVUt1dXVeuVUlKWSoh0Ohg7IqwKeftbOMaCB4AKFT6Jg1yw8hAFLt0qVLtmrVKm+VodZlR5qoPEvPTRWioX/apUplVVrNqcnUcSCi5s2bV/RcnSQjeARUi1+j4UlIgcFBv+yKLZqB1NLqxooVK+zpp5+OxEX5+vXrbUmFduBTj4p6VVRWVequXJGnWQzM90KJKvnzFmcEj0BDg9nYmDsAQrBxI9PNgZRSv4MuzI8ePerO1F4l7sAGU8dVNqZtQxNNm4aodJZyGZSg0iuMcUXwEN3FoOkH1aC7Zdpqt8oTggHUhlY2ND1c5VW17ufIVU7NucqqduzY4ZVVacJ6asqqFi/WrWt3AExPGD1VcUPwkHnzzLZvdwdAyBYtMtP2lYQPINHUw6Fejp6enshtIzsxMVHS3VcFDAUN7caluSOJLasqZHzcr5AIee4Jkok+D4KHv9rR1OQPfQOqQd9rCh4KIHzfAYl07tw5b1engYGBsoYChmXjxo3W2dnpjoqjUiqVVClInThxwp1NoQULWPVASXp7e1Pf50HwWLiQIW+oPt0ta2kx6+52JwAkxdjYmNfPoV+javHixV74KEYwdVyrHKkqqypEqx7Nze4AKN7IyIi1qtw6xdIdPFRnp0Yxmn1RC2pU1GrbypXuBIC403Tu7u5ur+k6yubOnTvltHQFjGDIofo51NcBR8FDFRPANCjE19fX28sprnZId/Do6WFrPNTW6dN+vfDAgDsBII7Uw/Hkk0/aunXr7EoM6v/V33FZNz8K0OA/lYqprEplY8ihvtCODncAFE8/e2keJJju4LF8ub9kCtTSxIQfPphuDsSSLsw1nyOq/RyiC51PfOIT9uY3v9luuukm+6Vf+iVbsGCBncwZbKo7spqqrlIxrYikvqyqEIVLSmVRgra2NhseHnZH6UOPBxAFKnmoqzMbHXUnAMSB5nJoS9lDhw65M9GzZ88ee9Ob3mR33323V2KlC593v/vd1tTUZK9//eu97X6zy6q06w5lVUA4VIqpJvO0IngAUaE7INreUisgACJPE8gVOqI0FDCXVjpmzpxpLS0tXuDIffzmb/6m3XHHHd5OO0888QRlVTGnncc+85nP2P33329f/OIX7f/+3//rfgdRsWXLFm+1Ma0IHkCUqG5Y4YPJuEBkZc/nUGlSlCkYvfWtb80bOoKHVj7uu+8+9ycQVz/84Q/tIx/5iH33u9+1X/ziF96MlT/7sz/zVrIQHfv370/1zlYEDyBqtAQ7eza7rQERpIs5rQyoDyKq/RzZ7rrrrmvlVYUeKrtSyRXibe3atfaNb3zDHfl+/OMf2xe+8AV3hCjQqlSD+jpTiuABRJG22NUdEQYMApERNJHv3bs3Nk3XaiTPFzZyH3o/xNv73//+yE3IR351dXWx2P0uDDzTAFHV3s50cyAiDh8+bI8++qi3zWyc/Mqv/AorHikxf/589xaiTuWNuTvKpUW6gocu4CbZtxyIlKtX/fDBlo1AzWhlY+fOnV4ZS9T7OfJRj8fb3/72vIEjeKgH5H3ve5/7EyiJri1qfJPoQx/6kP3sZz9zR6/Idw61pR4P9XqkUbqCh+YktLS4AyAGFD7mzGG6OVAD2lJ2w4YNXk9HHLeXPXbsmH3yk5+0173udfZbv/VbeUOHmsrf+MY3pvbua8UsXKix9e6gNj7/+c/f0OOhCfof//jH3RGior293du2Oo3SFTw6O/3GXSBONN28qcls/Xp3AkDY1M+h/fZ3Zy4m4zZE7/nnn/cC06pVq7xGVs3x+Bf/4l/YPffc4wUNBQ6VV/3Gb/yGt9VumoeZVYxCR+bzWks/+MEP7D/8h/9g3/ve97zjH/3oR/aHf/iHfH0jKM2zPNITPHTnuL6enYIQTwof2mZX2+0CCJX6OaI+nyMfNRYrKKkXZd++fdcFJs3z0J1vzexQI7kGCuabXI4yRGArdIWOP/qjP/L6PT784Q97wyERPevXr/fCRxqlJ3gMDvr18kBcBdPN9SuAUGgo4OOPPx67QXpHjhyxxx57zAYGBiYtC+vs7PQGmCEEXV1my5e7A6Cw7du3ez+LaZSe4DFvnmWekd0BEFPqU9L+3+Pj7gSAStDWlprNoX6OOG1zeebMGe/fvGbNmqLC0qJFi7xwghDoeVmrHindJhXFGxwctIXqC0qhdASP48f9O8U8GSAJdNGgFzeVXwEomy7YtVqgZs+49HNoVUO7bS1btswOHDhQ9L9b/R3q+UBItBkIPRWYQpqnl6cjePT0+PMQgKRQU5oaztkeGiiLdn5ST8TBGJUwKmgocCh4THe3rdmzZ9vExIQ7QsVpE5CU3slG8fQz2Nzc7I7SJR3BQ19clagASaItdlVCqI0TAEzbSOZ1QaHjdExWD0+cOOHNE1m3bp2dP3/enZ2exsbG2Px/Y0nN5SFVWGiDgCVLltgv//IvexsEvPnNb7aHH36YDQJiSD+D+llMo3QED5WmMP0ZSbRggVlHB9/fwDRolaCvr8/rjXjhhRfc2ejSv3fbtm22YsWKsnfaInhUgQbDVTh4KCTX19fbr//6r1+bRK8tkTWf5a677mLL3JhRiGxQv2YKpae5HEgirXZo73immwNF0UqBLuC3bt1qL730kjsbTerbCFZltNtWJf69dXV1sWqeh3+RqiGQLS0tXuDIfWjrXIUPVj7i42rmtXvGjBnuKF0IHkDcqc9DE/kZMAhMSv0cms/x7LPPujPRpcF/2qlq8+bNdunSJXe2fCrRQbx84AMfsLe85S15Q0fw+J3f+Z3U7pIUV2n9WeQZCEiCCxdUQ2HG/vxAXlo5eOSRR+y5555zZ6Lp4sWL3tRxhQ71dFQawSN+VGIVlFcVerznPe/xptMjPggeAOJNddszZzKvBsiiciX1R6xatarkhuxqUBlVMHVcO2yFta0vwSN+9DXLFzZyH3xt44XgASD+NMCqvp5d3IAMrR5oCrnKlV588UV3NnoOHz58bep4Jcuq8uHiNH7U3zHVioeazFnxiBeCB4Bk2L3bDx/s1Y8U00RvrR4888wzkR0K+Pzzz3tlVdoiVz0d1UDwiJ/f/d3fnbLH49/+239Lj0fMEDySRmUnbDGKtNq+3e/5YJcTpNChQ4e8AXtjY2PuTLRoe1xNSVcwUu9JNYMRu1pVWQVuAGm3qte+9rV277335g0dv/3bv22zZs1iV6sYYVerpNEWo6p1Z69ypJl2udLwzIsX3Qkg+Xbs2OFd0GvFI4pUVqV/n7bzrUUAYI5HFelaJBMIKvEc/Ld/+7d2++23eysf9913nxc4NMfjnnvusTvvvJM5HjHDHI+k2bPH314USLslS/yfBe5wIuG0iqCSJZUuRXEo4Llz57yBhT09PV6JVa0QPKqss7Niuw3+8Ic/9GZ2vOlNb/LKdN7whjfYBz/4QVY6YojJ5Umji63Vq90BkHKq+9WEc0oPkVBa3VBz9q5duyLXz6FApFWYoPSr1v++2bNn2wT9X9Wjnru2NncA+PQz2KyKhBRKZvBoaqK2HQgocLS2+nfegITRUMDu7m6vhClqtC2uAocCkQJIFKhEZ4+qAlAdWm2uq2PVGdfZv39/5mU587qcQskLHrqTM3u2OwDgCaabL1/uTgDxpx2rFDrCGLRXjlOnTl0r+4paWdOiRYu8bXtRRVpxHhx0B4C+HQZTuwtZ8oKHGmopswJupPChmtKNG90JIJ40bG/Tpk3eUMCw515MR1BWtWLFilCHAJajs7PTtlSo5wBF0nMuW90iy/bt272fxTRKXvDQXd39+90BgOucPWumnTTYAQUxpcZsBQ5NI4/KUEAFjH379nllVTt37oxk4Ahohai3t9cdoSouXPBnK2mXKyBj/fr13s9iGiUreAQXVTTRAoUdPOj/nIyOuhNAPKhsSRf3Bw4ccGdqT2VVmo6+bt26SK2+FJLmC56amjPHbGTEHSDt0nwDIFnBQ7W0LCEDU9OqoPaXHx93J4Bo01BAzb+ISj+HtuzVLA79m9TgHhe7d++29vZ2d4Sq0XNulabTI/r0M6ghommUvFIrAMXRNo9a+WBPf0SYypbUN6FVhfPnz7uztaN/T9DUrqnjUSn3KpZ6T+bOneuOANSCdrTSzlZpRPAA0qyvz284Vw0yEDFaVQh2h4rCdrTHjx/3ApBWOmo5BLAcFy9eTO3EZCAqmpqaUjv4keABpN3KlX79ceaCBIgKDQXU7lBPP/10zZu1dbHe39/vNbUfPXrUnY2vuro6e5leSKBm9DN4JaWzXQgeAMwWLzbr6GBjBkSChgGqify5555zZ2ojKKtSH0cUAlCl6G4r08uB2tDKaZpXHQkeAPzAMX++H0CAGlLDZRT6ORR6HnvsMevr60vcnckFCxaktrEVqLU0Ty0XggcAn/aYV9OpSq+AKtNqwpNPPukNBqxlw7Z6N9RTotARtYnolbIy8zO+kUGiQE1ogKfCf1oRPAC8QtPNm5qYbo6qUg+F+jlqORRQ09C1CrB06VJvGGBSyqryCf6fAKov7UM8kxE8enrMxsbcAYCyaIcr7XTFTBxUgZq19UKsOR21op4SrXBotyrtpJV02k0nzaUeNaXBreqnQ2q1tbXZ8PCwO0qfZASPlhZmEQCVpEFXGjCY0n3GUR3BPAxNJK+Fc+fO2RNPPGE9PT2JLasqZFbm5/uyVjhRXdo9sL7eL21FKuln7+zZs+4ofeIfPPTF091ZAJWlO3MKH6wmosJU1rR582Zbs2aNV2ZVbZoJoqGEaSirKkRDBDVMEDWg7ctHRtwB0kTPd/WZ4Jnm7azjHzxUDpLiJh0gVHpxVPhI6aAjVJ5eeLVrlYKHAki1KWgocCh4RGEoYa0sXryYBvNaWb3aMt+E7gBpMpJ5TU17mWP8g0dnpz99GUA4BgaYbo6KOHbsmDcTY+/evVVfZTh16pQ3BV1lVSqxSjuFjk69fqL69uzxdxBE6qipfMmSJe4oneIfPLQDTw2W6oFUCaabUxOOEqmspxZDAdUsrqZxBR79G9JYVpWPBgiq1hw1oLkwdXX0eaTQvHnzUj9DJ97BQ3dgZ892BwBCpbujbW28WGJadKGvbXK1Xa5mZFSL/l41r6usSi/0aS6rKqQuc/F7gZXM2tCmOOqjQ6rwMxf34KH6VJaKgepQM1x7u9miRf7bwBS02qDSJq04VHM+x/Hjx70+Eu1YRVlVYdx9rSH1eKxf7w6QBuPj46wyZsQ7eCh09Pe7AwChU+BQbfLixYQPTOrMmTNeadWuXbvcmfCpcb0/85qgLXo1mwOTo968htQ7x43TVFmfCZr0VSWhx4OyD6C61OehMgE2dUABQT9HtYYCanes3bt32yOPPOLdwa/V9PO44Q4sUD2sMPriHzwAVJ9qVLWxAyuOyKK+ioGBAa+R+/z58+5suIKp4xs2bKhqD0lSUHMOVMfMmTNTPTgwQPAAUBpNN888kTIIC6J+DvVU6HHp0iV3NjwKGQobKquq9k5ZSdLe3u6VpwEIz+joqDU3N7ujdCN4ACjd+Lg/44Pp5ql2+vRpLwCojCDs7Wq1O5X+nocfftgrr6KsqjyDg4M2f/58dwQgDKtXr/YeIHgAKJeGYWnlQysgSB31cai3Qn0dYQt6R3SHnrKqylDph8qtrtIvCYRGqx379+93R+lG8ABQPjWaaxmZWvHUCPo5tNKhFY8wBVPH1ctBWVXlzZ4920YomQRCcfLkSauvryfcOwQPAJWRuQD1wgfTzRNP5U7q5dCMDm1hGxb9PTt27PCGAGoYYNhlXGmlbXUXLlzojgBUkn6+2Eb3FfEMHnqh4+IGiB7N99CQQWZ8JJYaxzWcb9OmTd42tmHZt2+fV8Klsio1riM8WrFSudXL/NxWn65lQgzvqD1to8uK4iviGTyWLzdbudIdAIgUBQ/CRyKpzElb5R44cMCdqTwNHlyzZo0XbjSBHNWhGnQujmpgcNCfYo5EUqhXmdVlbpZfE8/g0dpqNjzsDgBEiupYNd2ciciJ8uyzz3orEGH1WFy5csW2bdvm/R26AKasqroot6qR0VH/+RKJtHHjRsqscsQzeGjS6smT7gBA5OjujgYM9vS4E4grBQCVVWkFIoydpPTxtYKiPg6VVVVjBghupN2tZsyYEWrPDvLQjRptSY5EmpsJlexmdb34BQ/tmlNfTxkHEHXa6Ug3CbZvdycQNwoaKnvavHlzKPMyVFa1atUqyqoioqOjg2GCtaCbNCHvDIfq025W2jEujb1T6svTboSHDx/2NgbRJiF6btGGJPELHrt3mzHsCIgHDRjUjQJKI2NHQUCrEGEMBdSqxtatWymrihgNE5wzZ447QtUsWGCZHzR3gKTQVuNJHBqYGyr0GhGECs1ZUmmZftWxzuv3tVmI3l9/Ln7BQ/MCaMQC4kM1zBowqF8RC+rnUOiodD+HAoZegIIhgJRVRYvuzM7M/KyOjY25M6gKlaT29roDJIF+lmbNmuWVMMZJECr03K/n6uxQoSD1h3/4hzeECoWPIFQUswNh/IKHmt8o3QDiRdPNVXalFRBEloKBGrw1qO/cuXPubGVodxfKqqJPgbOrq8sdoSq0s1VHhztAEgwPD9v8iFXnaPvz8+fPXxcqtPK8YcMGW7FixXWhQudUHpUdKtT/VYkt1OMXPLT7w8GD7gBAbAwM+E2UNK9Gku5UaTr4unXrvB2mKkUfV3fGFDqOHDlCWVXEjY+Pe6seTFmuIgXxlhZ3gCRQv5Qu7KslO1QczFwjB30V2aFCD72dHSr0vvoz+rNhzmXKFr/goTsx7IcMxJPKCVRDTviIlBMnTnh3ugYy4bBSLz4KGHv37vWW5+njiBftxLOdyoLqUdBnlSkxtKKrMqtKhfcgVOjjZjdrB6FCz93ZoUKrGEFfRbVDRTHiFzwAxJvme2jlkjuqkaA7XmryrmRdv14g9SJIH0c87dmzxwsfAIozvHOntbzxjVZ30032GzffbI+/4x1F7b6qQKASpuxm7ewdoLJDxRNPPHGtryI7VBTTVxElBA8A1ad6ZtW/Ej5qamfmxVIvaNrWthKyy6ro44g3bQPKJHNgaurnaLz9dtufCR2WeYxmHo2Zx9987GMFVyqyQ4VWhbObtRUqptOsHTcEDwDVpztBuqOaecJF9WkmR19fnzejoxL9HLprp4vURx99lLKqhNDWum1tbe4IQLag/EmrDm9varJ9r3qVFzqCh8JH06tfXXClIqmhohgEDwC1oV6t5mazlSvdCVSDhgJqRaJS/Ry6m6ddsPTCSllVcmg70MbGRrbWReooEAShQkFh9+7dkzZqv/a22+wXmZCRHTz0mHHzze4jIhvBA0DtaI9zbbObuWhF+HQRqX4ONX2XS3XJmzZt8rbHPXbsmDuLJFGY1O48QFJkr1QUChUqgQpChX5P75PdU5F7w6alpcX2v+c914UOrXg033mnew9kI3gAqC31AjQ0+HvZIzRPP/20VwqlHazKoTIq1SqrLlmDBimrSq5g1UNb7AJRF4SKYnd/KiZUFEM9Hv/yV3/Vnnjta72Vj9G6Omt8wxtsaOdO9x7IRvAAUHu6sFH4oKyj4tTDoX4OlVeV28+hF2e9aKtMK631yWmjbXUrNQht//79Xt/IgQMH3BmgOAoE+XZ/UoCIwu5PDz30kL3xjW+0GTNmWHNzs/d3I7/4BA9dkGgAGYBkCqabT0y4EyiXXmz1Qrx582b76U9/6s5On17sNVxQ4UVvIz2CVQ9tu1wufQ/19vZ6vyKPjRtTOyBZoSA7VOjCXeFhqt2fFCpq3aiteR2a28HKYHHiEzxUA754sTsAkEi6udDUZHb6tDuBUmlKeLn9HFoh0V3FpUuXei/ylFWl05YtW6y1tdUdleb//b//Z/fff7+3o1p7e7t3jByacaTwkTBBqFBI0PNIdqhQmAj6KrJDhcJHXLaU1b97wYIF7ghTiU/w0M437H4DJJ+mm2u3K6abl0zzOfRCfvToUXdmehQwdIGgj6GyqnJWS5AMmuuhWvZSHTp0yD772c96b6/MvJZ/5zvf8d5GFj33LV/uDuJBoUArq9mhQpOzc5u1dXEe9FVkhwqVT5XSVxEVly9ftpkzZ9ppbpYVLT7BQ6sdW7a4AwCJ1tVlpjushI9pCeZzqJRF2+aWQhcD2qlKddLnzp1zZ5F2asJV7XqpfUIqsdJEdPnGN77hHSOHVnwXLXIHtRc0awehopgdoBQqVJYX9FXEOVQUY8mSJZnLU6pxpiM+wUODjNyTFoAU0JP5vHmq93EnMBndOVQPxpNPPlnSi73uXOpOpWZy6KIByKUmc5XCTNcvfvELe//73+81lgcPlVvpPLKoR2DOHHcQriBUVHsHqCQ5efKk19uhVQ8ULz7BQ02nLGUB6ZK5OPHuAGrSOQrSFrm6UChlaniwPa7+vC4stGoC5KPmWZWVKOROx+joqBdos6m2X+VXyKLPa+bzWwlBX0V2qMht1laoqMUOUEmhGTes3E1fPILH1atmt9ziDgCkhlY7WlpiV/dcTdqaVM3fusCYLt3tVFmVLjxKLc1CuigwTLeR9gtf+MINW+hqa91169a5I1wzY4Z/zTOJ3FCR3aytUNHZ2en9mt2srVAR9FUQKsqnbaY1OFA7WmF64hE8Tp709/gHkD5axp4922z9encCojIHXVTorqXuUE6H7ljrz1JWhenShZa21w36NaaicqqPfvSjN5RV6fiBBx6g3CrHC/fcY6e++U3v5zJo1g5CRRJ2gEoC/Qyo30kreZi+eAQP7Wtd5lZ+AGLs7Fm/3HL7dnci3XRxoQZy9XNMZ8epoKxKE8z1K9vjohQKHQ0NDdS2T1PQV5EdKm7YASoT0noyASO7WTsIFXHfASopFAAXLlzojkKgiec3ZS7Pv/pVdyJZ4hE8LlzQuqw7AJBKarxU+BgZcSfS6cyZM9f6MaYTHHSxoxUO3SXlrijKpd18VNIDX3ao0K5OCgzZzdoKFbnN2nqfG3aAOn7cv+ZBJGmVQw3lZ3UzLCwKNeptDDPc1FA8ggcAiJa2FT7GxtyJClKgueces1tvNXvnO8327XO/ER2qk9dQQA0HLJbukupCR70c6ukAKkHb6jY1NXkbGiRdECqK3QFKqxhBX8V1oQKxpin+KrEaHBx0Z0KgjVRuu81MK9m3357IjVUIHgDiJfOC7oUPrYBUij6W+si+/W3/WKHjrrvMvv99/zgCnnrqKW+JXxcxxdCFjlZFVFalCyDKqlBpCh26+1vqbI8o0M+JwrlKmbTLlv5PGpoZ9FVkhwp2gEo3Pf9qJ6tQfe1rZr//+/7b73ufBuj4bycIwQNA/KjRXEGhUltsa0n7K19xB862bWYf+Yg7qB0Fhk2bNtmaNWuKvsDRXVmVVenOKxdFCNOiRYvsD/7gD+yP//iPvRBy00032Rve8AbvvOYc1JpChbabDlYqNNVfvVHqkVIo1wqiLiiDnimFCoUPmrWRTSVW6mu6EHYZnEqsvvxl/229Buk4YQgeAOJp5Up/2FYlGlxf//obt7DUUvcdd7iD2tAWtwoculgqZsVC769SD92p1cUWEDatqt1666321re+1ebOnesNB3z3u9/tlWEpgHxNd3BDoo0V1PN09OhRbwVCoWHz5s3eyoSC90MPPeRtNa2fIZ3XSsazzz7rvb9+Pi5dusRKIKYU7GJV7E5uJdP3ol5z1FgePFRulbDvUYIHgPjS3aDMhU7ZdbB6gs9H/R41onpy3ZFV8+lUdAGmiy5dZFFWhWpRg+2dd95p995773VTyYPHb/7mb1p9fX1JKx/6Hg5WK1QCFfRV9PX1eWVPDz/88LVQoXkgWt3TSkXQrK0/y88BKkEbKeh7LXTDw/7rWbb3vMcvv0oQggeA+FLgmD9fI2TdiRJpxeOf/9kdOFoBqdGKR9CbUcyqhUpC9L66KJvO1rpAuT71qU/ZO97xjhsCR/ZDKx/333+/+xM+lS+pN0IBQUFZ3++5O0Bll0Bt27bNdu3aZXv37r3WVxHnvhLEhwYFzpkzpzrfbw89dOMWutpaN3v3uB/8wO9xjDGCB4B4U/iYO1e3pdyJEqiXI6irDXzpS1Xv8dAdWjWvqlRkqtryc+fOee+nsiq9DVTbXXfdda28qtBDZVe33377daFCDdvBDlAKHAoe2c3a7ACFKBgfH/f6lqqyG6BW597ylhvLqnTc2Oj/mnm+t3vvLbxCHxPR/9erkacaS1wA4kt9Hur3WL3anZimiQl/F6vvfMc/1q86ruTOWVNQ0FCQ0IXYZCUiWtXQ+wRlWJSToFr0PaqGa62yKSiokTxf2Mh96P0IFdOgzS7CnBOBKWk4pvo6FIojY+tWP4AQPEKmpKm7mQAwGd2k0J2h/n53Ypq+9S1/fof6Ot71Lv+4SnRRprIS1bJPRkFDgUP9HJRVoZKyQ4X6KfQ9Fmwpq+/NYKVCxzqv8PumN72pqBWP16uUEcVrbWVoco3Nnz/fli9f7o4ihuARMv3wzZvnDgBgElqhmDHDb9KLCYUJ1bMrfBSiC0LVumtFhLIqTFcQKvQ9Fuz+NFmo0O8rfARbyqpRO99KRak9HpiC+tZi9ByWNL29vZns12oaGBhJBI+QKXgkcB9jACHRlod1df6U8whTiZS2yVWtu7bBzScoq9LWoLoIBHIpVGQ3ais0aIen3J4KhYqgp6KYUFGMYFer++67L2/o0PlSd7VKNTUTb9/uDlBN2nJZYVk/F5FF8AhZ5pvguo5+AJhK5uLLZs70SzUjSPMDdCGowYCFSqZ0EaktHHUh+eKLL7qzSBMFgql2f8pt1FaoCLaUrUZPhWYbvPnNb/bq4YMAovKqu+++22bMmGHvf//73XuiaIsXm23Z4g5QLfq50ZDAqjSTl4PgEbKNG82iWmcHILp0x7CpqXLTzStEA89U3qKLyHyN4dpCN7g7XWglBPEXhApd5AR9FdmhQoFCwSI7VER19yetfDzwwAPXTS5X4Pj+979vLS0ttrrUTR/SSp8vPmdVpe/hxsZG209vTeiiHzz4AQRQKt20mD3bLCLL5mNjY17oOHbsmDvzCpXMqERGF5p6P8RbbrO2gkPQV5EdKtS3E/RVZIcK/fkkCHYH0jwEFInrnqrS96gC8hZWmaoi+sFj5Up+AAGUTj1i2qBCAwFr6KmnnrJVq1Z5F5XZtOqhC1PKquIjN1To65YdKjo7O6/1VWSHiqCvIimholjB3eTBwUF3BpPq7aXSo0quZl4XtDMbq3LVE/3gQa0jgHJkTzevwS4l6uFYt26ddxGaGyq08qEwolKa3ECC2ghCRXazdhAqitkBKm2holhqMFcp1mjEN32IBK0O0dsaOu1apW1zu7q63BlUQ/SDh0oO2BEDQDm02tHWVt508xIoTDz++OPeTinZ9fjaErevr8/7vXxlVwhHbrO2QkO1doCCPwlazbsjIyPuDPLSTKKoNzjHnFY6Fi5c6K1ORnbb3ISKfvAAgErQdPOWlqqVbh49etSbz7F37153xl/90Ba6KqvSxRdTxysnO1Rod5qgryI7VOQ2a+t9qrkDFPydg7TF7jBzKlAjCh3t7e22YMECQkcNEDwApIfuJM6aVfp08yLt2rXLmzCuu+SBAwcOeOdUnqPtdFG8IFQUuwOUVjGCvgpCRfRoC16FD+3SBVSTgkZHR4e37bMCCKqP4AEgXTTdXDM+Qrjjqh4OBQvtVBTU+uuiV8cqq4r8/vA1ktusndYdoNJE25bOzPwcspMQqkVBQ6schI7aIngASB/t1V7h6eaq/9fFsS6aVUKlEKK3VW6V5rKq7FCR26ytUMEOUOmlng+FD3a7QtgUNNRIrucbQkdtETwApNOePX7ZVQVWIdTPob4NXTCLfk1DWVUQKrKbtfV/1sqEQlh2s7bOB30VhAoEJiYmrKmpydtsgXp7hEFzOrRlLo3k0UDwAJBe69ebNTaWNd382Wef9VY1NPRPu1XpIjsJZVXZzdpBqCh2Byj93+mrQLE050NDBrkwRKXpe0vDAVeuXMn3VkQQPACkW+bCuZTp5iqd2rZtmz322GPei5suyuNSVqWVhuxQoSZfBYfsUJHdrB2ECnaAQlh0V7q1tdWrwacUBpWg1TQNrtRqGqIj+sGju3vaFwQAMC0aVDqN6ebPP/+8rVmzxjZt2hS53arylT/lrlRkhwp2gEJU6I704szPospi1DOVWvq/69oHJVPfkAZWsnNa9EQ/eNTXEzwAhG/BAm+6+dnTp63rYx+zxje+0W666SablXkOWvLgg97kZdFFvfo5/ut//a/XehcURKohCBW5jdrZPRV6aMJ2brO2QgV9FYgDfe9q0KDKF1NJM4d07YOS6HlPmxYwJT+aoh88Mi/8ABC6K1dsz913W8Ott9rqV73KJvTck3mczDx677jDGt78Zvv85z9vn/70p+0v//IvvRWPSvZxaLjg6Uzo0cWWypqCUKGLMAUJBQp2gEJa6Hs71XesufaZNpXoLVq0yGbPnu3tmIZoIngAQIb6NBpuu80OusCR+zhyyy1Wn/n9hx56aNp9HFcyoUarIkH5k6aXB+VP6hHRx1So0EqKAo1CBTtAIe0U7HURqZ+L1DUG63kHRbtw4YLXRK4eoVSX6cVA9L+z+eEDUAVd73ufrc4KGvkef37HHfbBD37Q/QlfsPuTLpIUEhQWFBrWrVtnq1atsocffvhaqAhWKgYGBrzwotUN/TmFkrTO+QAmo6ZzXUyq7yMod0wFPeegKMHqWG9vrzuDKIv+dzY/fACqoLGu7lp5VaGHyq5en3m/v/iLv/BWKlR2pdWKT33qU9eazRU6FCq0A9SxY8e8u2+ECqA869evt/r6ehseHnZnEk7POZiUVsFWr17t9QPt0VwmxEL0v7P54QNQBWokDwLGZA+935/+6Z/a5z73Ofvrv/5rr2Tqqaeesr/5m7+xp59+2r7+9a975VSHDh2y//7f/7s3XFAlVv/7f/9v747tD3/4Q2/eh1Y5VD6lMizVJrPHPDA5rRCq9Eo7X2klJNH0fIOC1MMxZ84ca2tr88qsEB/R/87mhw9AFRS74lF/xx1e2Pirv/orr9l87dq13sDA5cuXe43fKqn6xCc+YX/0R3/kvf2Zz3zG+z2tiOh91ZiuP7t582ZvdUSBRQ20Cizf/OY3vcCiC6zswPJ//s//8QLLP/zDP1wLLP/0T//kBRa2vkWaKHCogVilNYle/dBzDm4QrHLUZZ6vtQrGzJf4if53Nj98AKqgmB6PtXfeaR0dHV4AUBBQKFCPhgKC7sBphUPBQbM9tPSvMPF3f/d3XrhQyFBg2bhxoxc8tAWuwohCyX/8j//RCym6k6t+kE9+8pNeiNHvKdQEgUV/Vh9j+/bt11ZYvvGNb3h/X7DCon9H7gqL/r26K6g5IwQWJIHKGTUcTj8viVz90HMOrqMbMmogV79PJXcURHVF/zs786QCAGELdrUaywkbweP4a17jbalbbIPriy++aD/72c+81Ymf/OQn3oW/SqwUBPQx9MKpVY0jR454geHv//7vvQChh8KEQoXChcq4gsCi8KEQ8tnPfvbaCotCii6+tMqi8PInf/In18KKwk2wuhKUhP3t3/7ttXIw/V3qRQkCi/49+ncFgeVHP/oRgQWRpTLFJUuWeDX+CiKJoucdeHJXOShLjTe+swHA2ZO5IG+4/XZv5eO4Cxwqr1rv5nhUo7RDF/aa6aHAogt+XfgrAOQGltwVFgUJBQoFiyCsKHAEqytBSZiCSVAOlru6okAz2epKdmApVBIWhJWgJEz/FwUWGuwRFq0uavVj4cKFydlKleDh0fOc+npY5UgOvrMBIItWPjo/8IHrJpcv/OAHi17pqBUFFl3ga2UiCCxBSZj+7QoG+UrCsldXFDImW10JAkuwupKvHCxYYQkCS/YKy2SrK5SDoRz6funq6vJ6P7RltY5jLeXBQ+VzWuXQBHJ9PVnlSA6CBwCkmFYigsCiFQqtVASBRSsY+QJLsLqSrxwsWGEJAstkKyzFlIQpGE3Wv5JdDhassBBY0kvfI/Pnz7fm5uZ4l1+lNHgoYChoKHCo5+306dPud5AUBA8AwLQVKgkLwkpQEqZyLIUGrXYU6l+ZrCQs6GHRrzrO18MSlIXp4wVlYfp7iulfoSQsmbRTnLZbbW1ttdHRUXc2Jq5cMaurcwfpoVJWBUZtkRu7rxmKRvAAAFTFZKsrk5WDBYGlUA9LUBamQBKUheVrutfvaSUmN7Dk9rF861vf8v7+oIdFgUX/tnw9LEFZGIElmrZs2WJNTU3eKoi+r2JBd/kbG91B8u3fv9/mzZvn9XGkZkBkihE8AACRNln/SnY5WLDCkh1YspvuFS4UMnIDSzF9LPkCS25JmP4+/d35mu71b9W/OTewUBYWPpXvKIBo96sFCxZ4X59IU4N8d7c7SC6VwmlFSqscChz0caQDwQMAkEjF9K8UKgnL7WPJF1gKlYQV03QfrK5k7xIWlIXl9rHo3xz0sRBYShf0D2gHLJXzJG4L3hjQ12BgYMCbx6HAoZ8HAke6RD94aGk0KdvjAQAiLwgsQQ+LAkuhHpagLGyyHpZ8Tff5VlcmKwfL7V/R36VHMX0sNN5fTxe6g4OD17Zp1cWvvt4Ij7Y57uvr88KGQod6cPicp1P0g0dbmzbpdgcAAERXoaZ7BQEFgtzAopWOYsrBJutfyS4HC1ZYCvWvBCssQWAppo8lyYFFqx4KH9pFSdvxRr4MK2b0fabvVQ3/6+jo8JrGWeFIt+gHj0WLLPPM6Q4AAEgeXdgHZWG5fSz5Aosu6PKVgwUrLNPpX5msJCzoYckNLIVKwuLadK//jz4nCiDaDUslWZolgenTLKTe3l5vRUl9NStXrvS+RwCJfvDIJGWCBwAA18tXEpbbw5Kv6T43sExWEhb0sCisFOphCcrCFFiCsrDJmu7zra5EpRwsKMNqb2+3GTNmeNPQNRmdu/ST0+dHDeJa1dDqhpr4tZpEORVyRT94LF6s/fDcAQAAKEe+1ZXJysG0yqHwoEe+HpagLEwBJCgLy9d0r2Odzw0shfpYsldXgsASrK7kKwer9AqL7tz39PR4fQm6mF60aBEX01n0edDnQ+FMnx+tFK1fv97r5wAKiX7wWL3afwAAgJrJ17+SXQ4WrLAEgSVYYQkCi1ZAtBKSG1iK6WPJF1gKlYQFgaWY/pViS8I0QVvlQ7q41kW25oJoi159rDRRqFAZmlaE9HlQOZWaxpkwjmLFI3isXOkOAABAnEzWvzJZSZgeQVlYvsBSqCQst4clX9N97upK8Pdll4QFPSz6N+rfGvSwKMj8l//yX+x973uf1dfXe30MS5YssaGhobKDiMqVWt7+dqu77Tbvol4fs5YUNLQDlT6fGsSo8jOVUynwpS10oTKiHzwyydortwIAAKkR9LAosBTqYQnKwhQWgrKwYpru862uTFYONln/yle+8hVbsWKF3X///fbWt77VCwwPPvig92f/23/7b95qkC7SFbqCFZZ8fSzDmZDRePvttv/mmzNXZzfZ6L/5N9b4q79atfChf5c+j1rJUZDSvBOtamjXL5Wc6ffodUG5oh88BgbMFi50BwAAAIXla7rXhb/KrHIDS3Yfy2TlYAoRQWDJ7V/JLgdTmNFDx/q9D37wg/bv/t2/8359+OGH7c///M+9AKSPv3///uv6WOa84Q22PxM4FDqCx7fa2uzuu++eNLCUQmFIf79CWXd3t1c6ppUbhSb1sqisTEFDfydQSdEPHpkfRuvqcgcAAADhyNfHMlnjvUqzssvBghWW3P6V7FKwj3/8414o+djHPmYPPPCAd6H/0Y9+1OpzQoceP3/Vq+zWW2+1L3/5y97qif6u3JKw733ve/ad73zH/v7v/977/a997WteKZj+DQpMn/nMZ7yejNbWVq9cSqsYChk6p9ChSeITExOsZqAqoh88AAAAImyyPpZCjfcKCV/96le9FZDPfe5z9q9uvvmGFY99t9xid9xxh33kIx+xP/iDP/DCih56+8Mf/rC3kvKBD3zAe7z//e+33/u937MPfehDXqBRuHnkkUe80LNhwwavhEq7UOnfoMCiEKV/W9C/Ukw5GFAuggcAAEANZPex7MqEicZM2AjCx2jm8auve50XGvKtsFRrDov+zqAcLGi4DwJLsEuYAotWiWo9hwXRR/AAAACIgOFHHrGWm2+2GZlH88yZNrRzp/ud6xUqCZus6V4lWgoSpc5hyQ0s2buEBdsaZ+8Slt2/krvCkrutsf4vCmCVnMOCaCJ4AAAARMWMGdpiyh1UzmS7hBUqB1OAKBRYsncJC1ZYCs1g0e/pfSZbXQn6V4LAEvSwKLDo36ZQlRtYgrIwAkt8EDwAAACiQqVWETJZ/0qwwpJvDktQEpav6T7f6spk5WAKOEFgCVZXssvBgoCkvzsILIXmsGQHFsrCqo/gAQAAEAUXL5otWOAO4m2yFZbJSsIKra4EgSW3fyW7HCxYYSm2fyU7sARlYbl9LPkCCysspSN4AAAAIBKCwFKrOSzZJWFBD4s+XqEeluySMJrupxaP4JH5Yma+gu4AAAAAuF6hpnuFAYWC3MCilY7JSsImm3QfBJagLEyBJSgLy9d0r79Df1e+1ZXscrDswJLEcrB4BI/MF9b6+twBAAAAUBnZfSzBKouCgB7ZKyzf/e53b+hhCcrCFDKCsrB8TfcKKQoruYElXx/Ltm3bbOfOnfZ3f/d33t/xzW9+0xsQqcBy5MgR+5//8396/65Tp07lDSw/+9nP7MUXX3T/u2iJR/Do7TXr7nYHAAAAQO0EJWG60A/CSm4Pi1Y0FBSC1ZV8gSVfH0tPT4+tWLHCPvWpT11bYQn6WHTuscce894nKAn7T//pP11XEvbMM89cKwn79re/fS2wBCVhQWAJSsJ+8pOfVG2FJR7BY3DQbOFCdwAAAADEj1YigsCiC35d+AeBpVD/igKEps4rUChYfPnLX74WVvr6+uwv/uIvbM2aNdetrjz44INeWNH0+mB1Re+j1RX9maAcTB8rN6zoEfSw6N9RqIclaLqfzhyWeASPzH/e5s51BwAAAEB65OtfCQJLoTkswerK7t27r5WDbdmyxVsl+cIXvnBd/0r26sp0+leCXcL0d2UHlkJzWOIRPM6eNWtocAcAAAAAppLdv5IbWLJLwhQSgjks0+lfme4clngEj5dfNm+gjn4FAABIGl3jjIy4A6C2wprDEo/gIbNm+SsfAAAASUN1BxJgqjks8QkeLS1mo6PuAAAAIEHoZ0UKxCd4LF9O8AAAAMnEDp5IgfgEDwAAgKRiZhlSgOABAABQa0uWmG3Z4g6AZCJ4AAAA1FpbGyXlSDyCBwAAQK01NZlduOAOpkHjBgo9JpPv/YMHEBK+uwAAAGqtsdG9UYZSQwNhA1XCdxoAAEAtXb1q1tPjDspA8EDE8Z0GAACQBLkBQsf5HrnynQNCEK/vtOPHzfbvdwcAAAC4ptQAQfBAlcTrO2142Gz+fHcAAACAawgeiLh4fadNTJg1N7sDAAAAXJMbIHSc75Er3zkgBPH7TqurM7t82R0AAADAU2qAKPTnfvADs1mz3AFQvvgFD614jI25AwAAAHgqGTyeeMLs3ntL/5hAHvH7bursNOvvdwcAAACouK1bzX7+c4IHKip+303a57q72x0AAADEmG6mRnnHToIHKih+303a2WrePHcAAAAQY+3tZkND7iCCCB6ooPh9N509S6MTAABIhsZGs/FxdxBBBA9UUPy+m15+mSGCAAAg/q5cMbvlFv/aJqoIHqggvpsAAABq4eBBs7lz3QGQfAQPAACAWujrM1u61B0AyUfwAAAAqIUlS6LdWA5UGMEDAACgFlpbzY4fdwdA8hE8AAAAqu3qVbMZM6LdWA5UGMEDAACgFk6fdm8A6UDwAAAAABC6+AaP0VGzjg53AAAAACDK4hs8Ll40q6/3ayQBAAAARFq8S62am/2VDwAAAACRFu/g0dlptn69OwAAAAAQVfEOHlu2mC1Y4A4AAAAARFW8g4eG7jQ0uAMAAIAYoD8VKRXv4CGNjWZjY+4AAAAgwhQ66urMrlxxJ4D0iH/wWLrUrLfXHQAAAETY/v1ms2e7AyBd4h88Bgb88AEAABB1XV1my5e7AyBd4h88AAAA4qKlxV/1AFKI4AEAAFANly/7/R00lyOlCB4AAADVMDJiNneuOwDSh+ABAABQDertUI8HkFIEDwAAgGpoamIEAFKN4AEAABA29XXMn2/28svuBJA+BA8AAAAAoUtO8NAE0KEhdwAAAAAgSpIVPGbONDt71p0AAAAAEBXJKrVS7eTgoDsAAAAAEBXJCh79/WaLFrkDAAAAAFGRrOBx8qRfbsWOEQAAAECkJCt4iCaCjo66AwAAAABRkLzg0d3tTwYFAACotd27zUZG3AGQbskLHpoI2tzsDgAAAGqotdVs+3Z3AKRb8oKH+jvU56EAAgAAUCsXL5rNmOH/CiCBwUOGh80uXHAHAAAANaCVjrY2dwAgmcEDAACg1jo6KLMCshA8AAAAKu3qVb/0++xZdwIAwQMAAKDStJvV/PnuAIAQPAAAACptwQKz/n53AEAIHgAAAJVEmRWQF8EDAACg0q5ccW8ACCQ/eJw+7d4AAAAAUCvJDh4aJtjQYDY+7k4AAAAAqIXkr3h0dfkPAAAAADWT/OAxNuavemj1AwAAAEBNpKO5vKnJbM8edwAAAACg2tIRPHp6zJYscQcAAAAAqi0dwePkSX8/be2rDQAAEIbVq80uXnQHAHKlI3jI3LlmQ0PuAAAAoIK0g6ZuctJTChSUnuAxMGDW0eEOAAAAKmj5crOVK90BgHzSEzwuXzYbGXEHAAAAFRLMDTt+3J0AkE96ggcAAEAYBgfN5sxxBwAKIXgAAACUY948s+3b3QGAQggeAAAApTp71qyuzuzKFXcCQCEEDwAAgFKpqbyz0x0AmAzBAwAAoFRtbWajo+4AwGQIHgAAAABCl97gMTzMkB8AAACgStIbPFpbmesBAAAAVEl6g4f23FZdJgAAAIDQpTd4qMyqsdHs5El3AgAAAEBY0t1cri3w9AAAAAAQqnQHjwsXzGbONLt82Z0AAAAAEIZ0Bw9pbzfr7XUHAAAAk9i/n4GBQIkIHnoCmTWLrXUBAMDUdMNyaMgdAJgOgoe0tPhzPQAAAApRiXZDg9nVq+4EgOkgeAhPIAAAYCrd3WarV7sDANNF8AAAAJhKsNrBhjRAyQgeAAAAU1m5ktUOoEwEDwAAgMloA5qmJoYOA2UieAAAAExm+3Z/NysAZSF4AAAATGZkxGx83B0AKBXBAwAAAEDoCB75aDmVOk4AAACgYgge+WzcaNbZ6Q4AAAAAlIvgkY8GCjY2suoBAAAAVAjBoxBWPQAAAICKIXgUcuWK2cyZrHoAAAAAFUDwmIwmlLLqAQBAuuzebXb8uDsAUCkEj8lcvsyqBwAAaaI+z4YGs7ExdwJApRA8psKqBwAA6aEeT6aUA6EgeExFqx6jo+4AAAAkFqsdQKgIHgAAANLby2oHECKCBwAAwIUL/mrHxYvuBIBKI3gAAAB0d/t9nQBCQ/AAAADpFqx2qK8TQGgIHgAAIN3Gx822bHEHAMJC8AAAAAAQOoLHdL38stm8ef6yLAAAAICiEDxKsXw5QwUBAACAaSB4lELNZzNnmk1MuBMAAAAAJkPwKNX27WYtLX7pFQAAAIBJETzKoeChAAIAAABgUgSPcoyN+ft+X7niTgAAgMhbv97s7Fl3AKBaCB7lWrDAbzYHAADRd/CgWWMjwwKBGiB4lOviRb/RnO11AQCINvVltrZSJg3UCMGjEhQ+AABAtG3caNbWxsYwQI0QPAAAQPKptEolVurPBFATBA8AAJB8Gvy7erU7AFALBA8AAJBsaihvbqbECqgxggcAAEguhQ2VWI2MuBMAaoXgAQAAku34cfcGgFoieITh6lWz0VF3AAAAAIDgEQbN9NCyLndYAAAAAA/BIyxbtpi1t7sDAAAAIN0IHmEJpqMODLgTAAAAQHoRPMJ0+rTZrFlmJ0+6EwAAAEA6ETzCtnGjWVsbe4cDAFANExPuDQBRQ/CoBpVc9fW5AwAAEApt6lJfT/gAIorgUQ0quZo50/8VAACEo6XFrLfXHQCIGoJHtRw8aHblijsAAAAV1dPjVxhQ2gxEFsEDAADEm0qrtJkL87OASCN4AACA+NIKh0qstm93JwBEFcEDAADEV3e32fz57gBAlBE8AABAPI2MmDU0mJ09604AiDKCBwAAiCcFjrExdwAg6ggetaSJ5hcuuAMAAAAguQgetbR+vV+XytZ/AAAASDiCR611dJitXu0OAAAAgGQieNTaxYt+Y9zwsDsBAAAAJA/BIwoUOjT4iH4PAAAAJBTBIypWrjSbM8fsyhV3AgAAXDM05FcJAIgtgkeUqN+js9MdAAAAz+ioXxkwMeFOAIgjgkeU6E5OY6PZnj3uBAAAKXf5st8LuX27OwEgrggeUaMnWAAA4NO288uXuwMAcUbwAAAA0dTbazZ3LvOugIQgeAAAgOjZvdsvP2bHRyAxCB4AACBaTp/2m8nHx90JAElA8AAAANGiHR77+90BgKQgeMQF9a0AgLTgNQ9IJIJHHJw8adbSwuAkAAAAxBbBIy60leC8edwFAgAAQCwRPOJkwQKzRYsIHwAAAIgdgkecKHBo1UP7mgMAAAAxQvCIG+1n3tBgNjzsTgAAEFNXrjCnA0gRgkccaV9z7W8+NuZOAAAQQ+3tZj097gBA0hE84mrPHn/lg52uAABxtHq1WVsbfYtAihA84uz4cfcGAAAx0tdnNns2N8+AlCF4AACA6lGPYmOj2dmz7gSAtCB4AACA6lBvIj2KQGoRPAAAQPhUHqzexJERdwJA2hA8AABA+JYuNRsacgcA0ojgkUSnT7s3AAAAgGggeCSRmvb6+90BAAAAUHsEjySamDCbOdNsYMCdAAAAAGqL4JFUo6Nm9fX+toUAAABAjRE8kkzhQ9sW6lcAAACghggeSbd/P3umAwCq4+WXzbq62OQEQF4EjzTQnumEDwBA2Do7zebPN7t61Z0AgFcQPNJizx52ugIAhKe722zePLMrV9wJALgewQMAAJRn+XKz1lazixfdCQC4EcEDAACUbskSP3RcvuxOAEB+BA8AAFCaxYvN5sxhpQNAUQgeAABg+rZsMWtpIXQAKBrBAyyPAwCmT1vn0kgOYBoIHmmn0KGtdrXlLgAAABASggf80FFfbzY87E4AAAAAlUXwgE9zPhQ+BgbcCQAAAKByCB54xeioX3bFoEEAAABUGMED1zt92qy52Wz1ancCAJBaek3QNHI2IQFQAQQP3EgvMNoisavLnQAApM7Zs2aNjWZ9fe4EAJSH4IH8tEXi4KA7AACkyvHjZk1NZj097gQAlI/gAQAAXnHwoN/vt327OwEAlUHwAAAAPu1sqNCh8AEAFUbwAAAA/qYiKq/SDocAEAKCBwAA8IPHxYvuAAAqj+CB6dOEc3Y5AQAAwDQQPDB92mIx2G735ZfdSQAAAKAwggdKo+12OzrM2tsZLAUAAIApETxQnpUr/QFT4+PuBAAAAHAjggfKt3u3v/2iej8AANFFAzmAGiJ4oDK04qFtGLu73QkAQGRcuGDW2kp5LICaInigcvRiNjjoDgAAkRDcGOrtdScAoDYIHgAAJNXQkFldnf8rANQYwQMAgKTRVucqfdXmHxMT7iQA1BbBAwCAJNF25+rnmDfP7+0AgIggeKB6aGgEgOrYsoUBrwAih+CB6jh5ki13AQAAUozggerZs8ds5kyznh7uxAEAAKQMwQPVpXrj+fP9+mOGWAEAAKQGwQPVp9WO9ev91Q/mfgBAaU6fdm8AQDwQPFA7Y2Nms2ebLV7s78ICAJiaAkdbm1lXlzsBAPFA8EBtXb1qtmiR2cGD7gQAoCDtVqXV4o0b3QkAiA+CBwAAUaeeuI4Os5YWBgICiC2CBwAAUbZ7t7/KsXKlv0oMADFF8AAAIKqWLjVrbjYbGXEnACC+CB6IvuPH3RsAkDJDQ2y+ASAxCB6IttFRv8Sgt5ehgwAAADFG8ED0nTxpNneu/xgfdycBAAAQJwQPxEdfn1ldndnq1TRYAgAAxAzBA/Gi1Q9tKdnUxOwPAPG3fbtZT487AIBkI3ggnvRi3dBgNjDgTgBAjOgmyvz5/k0U9bIBQAoQPBBfGqilBwDEhcpEVS6qTTP0KztWAUgRggcAANWwZ48/ebytjenjAFKJ4AEAQJi0ytHV5ZeHai4HW4MDSCmCB5JLdxR5gQdQa3oe6u6mNBRA6hE8kFytrf5jbMydAAAAQK0QPJBs/f1+ecPChWZnz7qTAAAAqDaCB5JP9dXLl5vV1zN8EEA4eF4BgCkRPJAe2cMHNQeE/g8A5dJ2uLqhMWsWPRwAMAWCB9Jn/34/gFy+7E4AQAk0wLSx0WzRIv/GBgBgUgQPAACmY2TEn8cxd65/IwMAUBSCBwAAxRgfN1uwwKy5mXkcAFACggeQD2VYAHJpe+716/2+DgDAtBE8gFy6izl7tllnJ3XbAAAAFULwAPLR1pgbN77SOKoSCwAAAJSM4AFMJgggGkLY3s4UdCDJuMEAAKEieADFUADRFHTNAFEAoQQLSI49e8zmzfNncdC/AQChIXgA06H+Dw0fvHDBnQAQW8PD/ra46umiaRwAQkfwAACkh3as6+vzA8ecOWyLCwBVRPAAAKTDwYNmM2eaLVzor3YQOACgqggeQKX19pp1dZmdPetOAIgE9WrRnwUANUPwACpN/R+rV/uNqmpEp5QDAACA4AGERndXBwfN5s41a272d8ViIjoQnosXWWkEgAgjeADVMDrqDyKcMcMvwwJQOSMj/s+XVhm16xwAIJIIHkA16W6sZgYAKI9KGjXcU6uJmsExMMCKIgBEHMEDABAfChjz55s1NPirh8ePu98AAEQdwQOIGpWKjI+7AwDX6e72Vw3VQwUAiBWCBxA1mqCs8hE9tDUvzbIAACABCB5AVGnY2dKlfsNsWxu7YiH5tNKnjRgAAIlE8ACiTjNANGVZu/Y0NvozQoCk0EC/nh5/hU8hu6/P/QYAIGkIHkCcKIRQeoW4O33aDxiacaMwvXixH64ZtAkAiUbwAJKGYIKoUrBobTVravJ3pFKTOGEDAFKD4AEkzYIF/lajuouswWqa5gxEhVY7CBsAkEoEDyCJJib8ZnQNVqurM2tv93fI0kUfEAaFCX3fseIGACiA4AEkneYd7N/vN/DOmePX1QOVoMZwzZ3R6ppW2WbP9r/XAADIg+ABpM2VK+4NYJpUtjc4+Mo2z3p0dPira6x0AACmQPAAcD3NUViyxL+TrTvaQGD3brP58/0dqfjeAABME8EDwPW0IqKtTbu7/bIsldBoJyLCSLJpOKUG+AEAEBKCB4DJqUdEU9TXr/d3zFJ5DUMM400lU9rxLPiaKlzq66oSKgAAQkLwADB9CiOT0Z1zlWxN9X6oHn0t1I+hGRra6Uw7niloqGdDq1hscQsACBnBA0DlaQetlhb/AleTqbWd78qVfqmWAokakbnQrRyFCoWHqYKeVjm05S2BEABQAwQPAOEJLoh1V11hZOFCP5CorOfCBfdOKIo+j+q90Q5SCnHawlY9OMHuUurDOX7cvTMAANFD8AAQPWpwV0mQLqYXLTJbvty/4NaKyZ49xd3djws1dRczeE9hQztKKXDobYU5ytkAADFC8AAQTVoRGRvzt3DduNEPHwoh6k0I+hSmolWWLVvMhob8wXZ66CJfE9yDRyn0b8v+GFPNRtH/QbuCdXb64aG52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<b style="mso-bidi-font-weight: normal;">OTRAS CARACTERÍSTICAS
DE LA INVERSIÓN:</b></div>
<br />
1. Dos pares de puntos inversos no alineados forman siempre una circunferencia. El concepto de potencia nos permiten asegurar que <b>dos puntos y sus inversos son concíclicos</b> (están en una misma circunferencia que es doble en la inversión y corta ortogonalmente a la misma). <br />
<br />
2. Dados dos puntos A, B y sus inversos A1, B1, las rectas A-A1y B-B1 son antiparalelas de las rectas A-B y A1-B1. Esto quiere decir que se cumple la condición angular que expresa la siguiente figura:<br />
<img alt="" height="276" src="data:image/png;base64,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<style>
/* Style Definitions */
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<div class="MsoNormal" style="background: #D9D9D9; mso-background-themecolor: background1; mso-background-themeshade: 217;">
<b style="mso-bidi-font-weight: normal;">INVERSIÓN
DE ELEMENTOS:</b></div>
<div class="MsoNormal">
</div>
<br />
<b>PUNTOS: </b><br />
<br />
La inversión de puntos se puede resolver mediante construcciones de potencia o con los denominados teoremas del cateto y de la altura. <br />
<br />
<span style="color: blue;">Caso1:</span> <b>Inversión de puntos cuando la potencia es positiva </b><br />
<br />
En este caso uno de los puntos es interior a la circunferencia de autoinversión y el otro exterior (o son dobles y están sobre ella), pero al mismo lado respecto del centro de inversión. <br />
<br />
Por ejemplo, conocida la raíz de la potencia de inversión, el centro de inversión y el punto A para obtener su inverso A1, podemos aplicar el teorema del cateto haciendo uso de la circunferencia de autoinversión tal y como se aprecia en la siguiente figura:<br />
<a 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ZDdjQ5iBtGJALIbGYg/pGByLfxsao+uEGRgJ7XKgcRXdLgdqaIwuEmZgpMRz53Y50HgeHc+l4/m0oTG6QpiBkRUxjkluy4HSJcIMdELc1m6XA43b3fGutOVAGUXCDHRO7x7S7dCY5UAZFcIMdJo9pBk1wgyMBXtIMyqEGRg77XKghsbISJiBsWYPabIRZoCGPaTJQJgB+ujdQzqWBLUcKMtFmAEWELe0YxONdjnQuOV96NAhQ2MsGWEGGFA7NHbvvffW59Ef+MAH6vPp2dnZ5gy4esIMcAUixrEcaMQ5Jrsj1obGWAzCDHCVzpw5Uw4fPnx+OdDdu3eX6enp5qdweYQZYBHFZHcsB7px48ayevXqsm/fvnLq1Knmp3BpwgywRGKKu53s3rBhQzlw4IDlQLkkYQZYBnFr+/7776/Pozdv3lyfT8/MzDQ/hQuEGWAZtZPdO3furJPdu3btKkePHrUcKOcJM8CQxBVzDI3FFXRcScce0lNTUya7x5wwAyQQk93xTnS8fhXPpOO297PPPtv8lHEizADJxIBYrC42MTFR1+2Of1sOdHwIM0BisWZ3vHIVr17Fe9KPPvqo5UA7TpgBRkA8dz527FgdFrOHdLcJM8CImW8PaZHuBmEGGGG9e0jHcqD2kB7cCy+8UO64446yffv2Mjk5WV588cXmJ8MlzAAd0bvSmD2kL+1Xv/pVjXJ7ZFnfXJgBOqbfHtJxVW1o7H995StfqUGOqff4z0ceeaT5yXAJM0CHtSuNxXPodmgslgON59Tj7OzZs/X2dRwvv/zy+X9nWNxFmAHGRDs0FleHEemI9bhOdv/617/+n6vkr371q/W/x+fDJswAYyhua8ft7XYP6bjtHbe/x2U50DbE8Zw5tM+bv/a1r9X/PkzCDDDm2qGxGBiLwbGuD4298sor9bZ1TGT/+9//rp+1E9rxefx8mIQZgPPiVat2aCxewYqr6q7tIX3ixIl6dTzf8dRTTzVnDocwA3CReO4ci5bEc+hYxCRuecfz6S4MjX3961/vG+T2iCntYRJmABbUTnbHRHc72R17SM/OzjZnjI64Tf3hD3+43rb+17/+1Xz6X/H/dMTnO3bsKK+++mrz6fITZgAGFkNj7faUcbs79pCOhTlGZWjsmWeeqVfF8Q5zP+27zXHesAgzAFfk9OnTdberjRs31t2vYhes2EM6c6S/+c1vLhjep59+uv78W9/6VvPJ8hNmAK7aqVOnysMPP1ynuuM4cOBAuqGxuD199913l4997GPz3qqOz++555563rBuZwszAIumXQ40bnG3y4HaQ/ryCDMASyKGxmIP6d27d5fXvva19Rax5UAvTZgBWHIR45jk3rlzZ72Svvfee+vrWJea7I4r7bj6XrVqVVmxYkWdCr/zzjvLH/7wh+aM7hFmAJbVzMxMOXz4cL3NHUNjcUXdbw/pmPa+8cYbyy233FK2bNlSr7i3bdtW1q1bV6655prygx/8oDmzW4QZgKGJAbGDBw/Wye52D+mTJ0/WK+WI9qZNm2qQ5x6bN2+ucY6hs64RZgBSiFeV9u/fX4Mct7tvvfXWvlFuj7hyfv/739/8dncIMwCpxGR3xLm9fT3fEbe145lz1wgzAOnEoFe/GM894ryuEWYA0nnb295Wr4j7xbg94ufXXXdd8xvdIcwApBPPmj/4wQ/2DXJ7xDPmWKGra4QZgHRiKvvNb35z+dCHPtQ3ylu3bi0rV66s63V3jTADkFK8x7x27dp65RzvPEeQ4/b1+vXr63DY8ePHmzO7RZgBSKtd+SueOceg15o1a8onP/nJTl4pt4QZABIRZgBIRJgBIBFhBoBEhBkAEhFmAEhEmAEgEWEGgESEGQASEWYASESYASARYQaARIQZABIRZgBIRJgBIBFhBoBEhBkAEhFmAEhEmAEgEWEGgESEGQASEWYASESYASARYQaARIQZABIRZgBIRJgBII1S/g+WzFI7E+gizgAAAABJRU5ErkJggg==" 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" 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" width="400" /><br />
<br />
<span style="color: blue;">Caso 2:</span> <b>Inversión de puntos cuando la potencia negativa: </b><br />
<br />
Una inversión negativa se puede obtener mediante una positiva de igual potencia (en módulo) más una simetría central. Aplicando el teorema de la altura determinaremos pares de puntos inversos.<br />
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<img alt="" height="322" 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<br />
<b>RECTAS: </b></div>
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<span style="color: blue;">Caso 1: </span>La <b>inversa de una recta que pasa por el centro de inversión</b> es ella misma. Sin embargo los infinitos puntos que la conforman y sus inversos no son dobles <br />
<br />
<span style="color: blue;">Caso 2: </span>La i<b>nversa de una recta que no pasa por el Centro de Inversión</b> es una circunferencia que sí pasa por el Centro de Inversión. <br />
<br />
<u>Se cumple además que la recta que une el Centro de Inversión con el centro de la circunferencia es perpendicular a la recta dada.</u><br />
<br />
<b>CIRCUNFERENCIAS: </b></div>
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<br />
<span style="color: blue;">Caso 3:</span> La <b>inversa de una circunferencia que pasa por el Centro de Inversión</b> es una recta que no pasa por el Centro de Inversión. <br />
<br />
<u>El caso 2 y el caso 3 son complementarios.</u> <br />
<br />
<span style="color: blue;">Caso 4: </span>La <b>inversa de una circunferencia que no pasa por el Centro de Inversión</b> es otra circunferencia homotética de la primera. <br />
<br />
<span style="color: blue;">Casos particulares del caso 4: </span><br />
<br />
<span style="color: blue;">Caso 4.a: </span>Como caso particular de éste cuarto caso: La<u> inversa de una circunferencia que pasa por un par de puntos inversos</u> es inversa de sí misma. <br />
<br />
<span style="color: blue;">Caso 4.b:</span> Otro caso particular de éste cuarto caso: La <u>inversa de una circunferencia cuyo centro coincide con el centro de inversión</u> es otra circunferencia concéntrica a la misma.<br />
<br />
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BIBLIOGRAFÍA</div>
<br />
<br />
<b><a href="http://piziadas.com/2012/05/geometria-metrica-inversion-en-el-plano.html">http://piziadas.com/dibujo/geometria-metrica</a> </b><br />
<br />
<b><a href="http://www.10endibujo.com/inversion/">http://www.10endibujo.com/inversion/</a> </b></div>
Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-46336830205911544802016-03-29T11:38:00.001-07:002016-04-04T09:03:47.917-07:00ENUNCIADO_INVERSION_EJERCICIO_1Determina la figura A<span style="font-size: 8.0pt; line-height: 115%;">1</span>B<span style="font-size: 8.0pt; line-height: 115%;">1</span>C<span style="font-size: 8.0pt; line-height: 115%;">1</span>D<span style="font-size: 8.0pt; line-height: 115%;">1</span>, inversa de la ABCD dada, en una inversión de centro
O que convierte el punto A en A<span style="font-size: 8.0pt; line-height: 115%;">1</span>.<br />
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrXmPJPiMH3HPz45jlMEH7YsvLN_liPcFCUOknffVVgA1pJQS5LJZS2ztPb2DNHzNM5r9yMsXviWjDmWXBLiDZIQ-nPKxViWmUsfEhsVtvwrdh2urvTQ5lpueWibamvghW_extRQJ7-UWV/s1600/Captura.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="347" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrXmPJPiMH3HPz45jlMEH7YsvLN_liPcFCUOknffVVgA1pJQS5LJZS2ztPb2DNHzNM5r9yMsXviWjDmWXBLiDZIQ-nPKxViWmUsfEhsVtvwrdh2urvTQ5lpueWibamvghW_extRQJ7-UWV/s400/Captura.PNG" width="400" /></a></div>
<br /></div>
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<a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span style="mso-fareast-language: ES; mso-no-proof: yes;"><a href="http://planolineapunto.blogspot.com.es/2016/03/v-behaviorurldefaultvmlo.html" target="_blank">Pincha aqui para ver la solución!!!!</a></span></div>
Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-35086905359750349442016-03-29T11:26:00.002-07:002016-04-04T09:02:40.515-07:00SOLUCIONES_INVERSIÓN_EJERCICIO_1<!--[if !mso]>
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Recordamos el enunciado:<br />
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
Determina la figura A<span style="font-size: 8.0pt; line-height: 115%;">1</span>B<span style="font-size: 8.0pt; line-height: 115%;">1</span>C<span style="font-size: 8.0pt; line-height: 115%;">1</span>D<span style="font-size: 8.0pt; line-height: 115%;">1</span>, inversa de la ABCD dada, en una inversión de centro
O que convierte el punto A en A<span style="font-size: 8.0pt; line-height: 115%;">1</span>.</div>
<div class="MsoNormal">
<a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqzTyeEQ5wj0Qp7pWAAABuAS59PRVQAUZ-HgMA1sWcBxiLNln_zYMA48-K6zn13kwoEmIcFmbbASsD4o7ZT4B0w3gVrgfhZHm1CBTCb7t3Sa9ZV17q52LGqcN9v-DPMlTo2GEu8xF86xa/s1600/Captura.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="346" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqzTyeEQ5wj0Qp7pWAAABuAS59PRVQAUZ-HgMA1sWcBxiLNln_zYMA48-K6zn13kwoEmIcFmbbASsD4o7ZT4B0w3gVrgfhZHm1CBTCb7t3Sa9ZV17q52LGqcN9v-DPMlTo2GEu8xF86xa/s400/Captura.PNG" width="400" /></a><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<span style="mso-fareast-language: ES; mso-no-proof: yes;"><br /></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
Sabemos que la inversión es una transformación en la que se
cumple que: </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
1- <b style="mso-bidi-font-weight: normal;">La transformación
es con centro</b>: Un punto y su inverso están alineados con el centro de
inversión (O).</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
2- La relación entre las posiciones relativas de cada punto
y su transformado respecto del centro de inversión se basan en el concepto de
potencia<b style="mso-bidi-font-weight: normal;">. El producto de la distancia de
un punto al centro de inversión por la distancia de su inverso al centro de inversión
es constante (K) y se llama potencia de inversión</b>. Por ello se cumple que:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="mso-ansi-language: EN-US;">OA*OA</span><span lang="EN-US" style="font-size: 8.0pt; line-height: 115%; mso-ansi-language: EN-US;">1 </span><span lang="EN-US" style="mso-ansi-language: EN-US;">= OB*OB</span><span lang="EN-US" style="font-size: 8.0pt; line-height: 115%; mso-ansi-language: EN-US;">1 </span><span lang="EN-US" style="mso-ansi-language: EN-US;">= OC*OC</span><span lang="EN-US" style="font-size: 8.0pt; line-height: 115%; mso-ansi-language: EN-US;">1</span><span lang="EN-US" style="mso-ansi-language: EN-US;">=OD*OD</span><span lang="EN-US" style="font-size: 8.0pt; line-height: 115%; mso-ansi-language: EN-US;">1</span><span lang="EN-US" style="mso-ansi-language: EN-US;">= OT*OT=K</span><span lang="EN-US" style="font-size: 8.0pt; line-height: 115%; mso-ansi-language: EN-US;"> <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Puesto que A, C y D están a la misma distancia del polo, la
única manera de que se cumplan las dos condiciones citadas es que A<span style="font-size: 8.0pt; line-height: 115%;">1</span>, C<span style="font-size: 8.0pt; line-height: 115%;">1</span>, D<span style="font-size: 8.0pt; line-height: 115%;">1</span> se encuentren sobre una circunferencia de centro O y radio el
determinado por el valor de la potencia de inversión.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>Puesto que en el
enunciado nos facilitan A<span style="font-size: 8.0pt; line-height: 115%;">1</span>,
punto inverso de A, los puntos C<span style="font-size: 8.0pt; line-height: 115%;">1</span>,
D<span style="font-size: 8.0pt; line-height: 115%;">1</span> estarán sobre la
circunferencia de centro O y radio A<span style="font-size: 8.0pt; line-height: 115%;">1</span>, que llamaremos c2. Por ser una transformación con centro, los
puntos inversos C<span style="font-size: 8.0pt; line-height: 115%;">1</span>, D<span style="font-size: 8.0pt; line-height: 115%;">1</span> se encuentran concretamente
donde la recta que une cada punto con el centro de inversión intersecciona con la
circunferencia c2, como muestra la siguiente figura:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=1732523761923805891" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoq62EyBB7idl0vfy0Llv6MCnkDsDp8KfYtbmjXGdIhi64ru31o9YnA02UnOENbDFAaNDjVPYopixnHKoKxS5Sa8jRJ6atFJPkWzLh7RVq0kr0aSexCzYCIw6Vb-sWe6HI28IsKuoUcDq_/s1600/Captura+3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoq62EyBB7idl0vfy0Llv6MCnkDsDp8KfYtbmjXGdIhi64ru31o9YnA02UnOENbDFAaNDjVPYopixnHKoKxS5Sa8jRJ6atFJPkWzLh7RVq0kr0aSexCzYCIw6Vb-sWe6HI28IsKuoUcDq_/s400/Captura+3.PNG" width="397" /></a></div>
</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"></span></div>
<div class="MsoNormal">
Ahora nos proponemos invertir la circunferencia c, sabemos
que:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">La inversión de una
circunferencia que no pasa por el centro de inversión es otra circunferencia
que tampoco pasa por O y que es homóloga a la primera.</b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Puesto que los puntos A, C y D pertenecen a la
circunferencia c sus puntos inversos A<span style="font-size: 8.0pt; line-height: 115%;">1</span>, C<span style="font-size: 8.0pt; line-height: 115%;">1</span>, D<span style="font-size: 8.0pt; line-height: 115%;">1</span> pertenecerán a la
circunferencia invertida c<span style="font-size: 8.0pt; line-height: 115%;">1</span>.
Tenemos tres puntos de la circunferencia inversa buscada, luego ya podemos
dibujarla. Observamos que la circunferencia buscada coincide con <span style="font-size: 8.0pt; line-height: 115%;">C</span>2. Lo cual nos permite
generalizar y enunciar la siguiente conclusión:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">La inversión de una
circunferencia cuyo centro y centro de inversión coinciden es otra
circunferencia concéntrica a la misma.</b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Hallamos ahora la inversa de la recta que pasa por los
puntos A y C, sabemos que:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">La inversión de una
recta que no pasa por el centro de inversión es una circunferencia que pasa por
el centro de inversión</b> y a la que llamaremos ac<span style="font-size: 8.0pt; line-height: 115%;">1</span>. Puesto que ya conocemos tres puntos de dicha
circunferencia O, A<span style="font-size: 8.0pt; line-height: 115%;">1</span>y C<span style="font-size: 8.0pt; line-height: 115%;">1</span> ya podemos dibujarla. Basta
con hallar las mediatrices de los segmentos O-A<span style="font-size: 8.0pt; line-height: 115%;">1</span> y O-C<span style="font-size: 8.0pt; line-height: 115%;">1
</span>y donde se corten se encontrará el centro O<span style="font-size: 8.0pt; line-height: 115%;">1</span> de dicha circunferencia.<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTZxivZ-s_ySJLugKgiAAZ4pEd0Pqxuw8oh-xPFb19eS-aJNmzHPUD6S67e4lUr2FU3H0Xx7cctjtdpCsRVZk2I9vusGNNOTBZueiS3Dn99aWlyNMmF6arcR4gDiwKogIvftOT2mt7JKhs/s1600/Captura+9.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="449" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTZxivZ-s_ySJLugKgiAAZ4pEd0Pqxuw8oh-xPFb19eS-aJNmzHPUD6S67e4lUr2FU3H0Xx7cctjtdpCsRVZk2I9vusGNNOTBZueiS3Dn99aWlyNMmF6arcR4gDiwKogIvftOT2mt7JKhs/s640/Captura+9.PNG" width="640" /></a></div>
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="mso-fareast-language: ES; mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
<span style="mso-fareast-language: ES; mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
<span style="mso-fareast-language: ES; mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
Finalmente hallamos el punto B<span style="font-size: 8.0pt; line-height: 115%;">1</span> inverso del punto B. Deberá pertenecer a la
circunferencia ac<span style="font-size: 8.0pt; line-height: 115%;">1</span> y
estar alineado con los puntos O y B, luego ya podemos dibujarlo.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Hemos acabado nuestro ejercicio, la figura inversa buscada
es la definida por los puntos A<span style="font-size: 8.0pt; line-height: 115%;">1</span>,
B<span style="font-size: 8.0pt; line-height: 115%;">1</span>, C<span style="font-size: 8.0pt; line-height: 115%;">1</span> y D<span style="font-size: 8.0pt; line-height: 115%;">1</span> y las circunferencias c<span style="font-size: 8.0pt; line-height: 115%;">1</span> y ac<span style="font-size: 8.0pt; line-height: 115%;">1</span>, o lo que es lo mismo, la figura resultante de la diferencia de
las circunferencias c<span style="font-size: 8.0pt; line-height: 115%;">1</span> y
ac<span style="font-size: 8.0pt; line-height: 115%;">1</span>.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
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<div class="MsoNormal">
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</style>
<![endif]-->Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-50218308743979969312015-10-23T11:36:00.001-07:002015-10-24T01:34:41.782-07:00<div class="separator" style="clear: both; text-align: center;">
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<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-38419112656026494982015-10-19T17:31:00.000-07:002015-10-19T17:33:59.673-07:00SOLUCIONES_MEDIATRIZ_EJERCICIO CAJA DE ESCALESRAS<br />
<br />
Trazamos el segmento que une los puntos I y J<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWVVvU1yQF7rwWRZonRjBnHGbXNQXSy_FU0YNEybDUZo8nvRhVxd5SW0Ev3yoMdIT8l5QMeG4WN3NdW6z5-wTAVv5_Mt-9S0bXvccja12n7m9yZ_FKME8YW-KIgaVQ3Q0uMdyVbriq6jSb/s1600/pasooooo+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="412" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWVVvU1yQF7rwWRZonRjBnHGbXNQXSy_FU0YNEybDUZo8nvRhVxd5SW0Ev3yoMdIT8l5QMeG4WN3NdW6z5-wTAVv5_Mt-9S0bXvccja12n7m9yZ_FKME8YW-KIgaVQ3Q0uMdyVbriq6jSb/s640/pasooooo+1.png" width="640" /></a></div>
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Hallamos la mediatriz de dicho segmento<br />
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Se trazan dos arcos de igual radio arbitrario desde los puntos I y J (radio > IJ/2). Los dos arcos se cortan en dos puntos L y K que pertenecen a la mediatriz, puesto que cumplen la condición de equidistar de los extremos del segmento. <br />
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Finalmente se traza la mediatriz, recta que contiene los puntos L y K<br />
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Repetiríamos la misma operacion con las otras dos plantas para acabar de solucionar el problema.Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-30980450043049857882015-10-19T16:28:00.001-07:002015-10-19T17:34:45.880-07:00MEDIATRIZ_EJERCICIO CAJA DE ESCALERASPara practicar el concepto de mediatriz resuelve el siguiente ejercicio:<br />
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Un edificio de viviendas tiene 4 plantas. Para acceder a cada una de las plantas, además del ascensor, hay una escalera que recorre todo el edificio.<br />
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La escalera es de dos tramos por planta y la meseta o descansillo de la misma siempre se encuentra en la mitad de cada planta. Por tanto, los dos tramos de escalera de una misma planta son iguales.<br />
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Sabiendo todo lo anterior, dibuja sobre el esquema dado y a la altura correspondiente la recta en la que se encuentra la meseta de la escalera de cada planta.<br />
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Unos esquemas para que te situes mejor:<br />
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Y ahora el gráfico sobre el que debes dibujar la solución:<br />
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<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-36923017478153610792015-10-19T16:12:00.000-07:002015-10-19T17:39:20.104-07:00MEDIATRIZ<br />
En esta entrada aprenderás:<br />
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1. Qué es una mediatriz de un segmento.<br />
2. Cómo se realiza la construcción gráfica de una mediatriz.<br />
3.Aplicaciones de la mediatriz en la geometría.<br />
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<span style="color: #45818e;">MEDIATRIZ DE UN SEGMENTO AB:</span><br />
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Es la <span style="color: red;">recta (r)</span> perpendicular a dicho segmento que pasa por su punto medio <span style="color: magenta;">M</span> ( M= AB/2).<br />
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Además la mediatriz de un segmento cumple que: cualquier punto (P) de ella equidista de los extremos del segmento A y B, es decir, AP=BP.<br />
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<span style="color: #45818e;">CONSTRUCCIÓN GRÁFICA DE LA MEDIATRIZ:</span><br />
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1-Se trazan dos arcos de igual radio arbitratio desde el punto A y B. El radio de dichos arcos siempre debe ser mayor que la mitad de la longitud del segmento.<br />
2-Los dos arcos se cortan en dos puntos C y D que pertenecen a la mediatriz, puesto que cumplen la condición de equidistar de los extremos del segmento.<br />
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<span style="color: #45818e;">APLICACIONES DE LA MEDIATRIZ EN GEOMETRÍA:</span><br />
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<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-25737155738712294182015-10-12T07:59:00.001-07:002015-10-12T08:39:34.968-07:00GEOMETRIA DINÁMICA_TEOREMA DE PITÁGORAS<iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/1805297/width/660/height/700/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" width="660px" height="700px" style="border:0px;"> </iframe>
Con esta geometría dinámica entenderás mejor el Teorema de Pitágoras. Arrastra el punto B con el ratón y comproborás que la hipotenusa al cuadrado siempre es igual a la suma de los catetos al cuadrado.
Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-9135839427222978632015-10-12T06:19:00.003-07:002015-10-12T08:28:22.956-07:00SOLUCIONES_TEOREMAS_EJERCICIO FOTO-LIENZO<br />
El problema se podría resolver graficamente gracias al Teorema de Thales. Recuerda que una de las aplicaciones directas del Teorema de Thales son las escalas.<br />
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Dicho teorema se enuncia de la siguiente manera: Si cortamos dos rectas cualesquiera por varias rectas paralelas, los segmentos correspondientes en ambas son proporcionales, es decir, se corresponden en la igualdad, en la suma y en la resta.<br />
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Aplicando Thales a nuestro ejercicio, para resolverlo, basta con: <br />
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<u>Para hallar las siete columnas del lienzo:</u> colocaremos foto y lienzo de forma que el lado largo de la foto y el lado largo del lienzo formen dos rectas cualesquiera. Despúes trazamos la recta que une los extremos libres del lienzo y la foto (P3). <br />
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<u>Para hallar las cinco filas del lienzo:</u> colocaremos foto y lienzo de forma que el lado corto de la foto y el lado corto del lienzo formen dos rectas cualesquiera. Despúes trazamos la recta que une los extremos libres del lienzo y la
foto (P2).<br />
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Ahora solo nos falta trazar paralelas a las rectas P2 y P3 que pasen por los puntos que definen las columnas y filas de la foto: <br />
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¡Ya está resuelto!, es fácil ¿verdad?<br />
<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0tag:blogger.com,1999:blog-1732523761923805891.post-78257959482566520652015-10-12T05:27:00.000-07:002015-10-12T08:30:32.760-07:00TEOREMAS_THALES_EJERCICIO FOTO-LIENZO<br />
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Después de que te hayas familiarizado con los teoremas de Pitágoras y Thales, te
propongo el siguiente ejercicio para que puedas practicar los conceptos aprendidos:<br />
<br />
Paula se ha apuntado a una academia de dibujo para aprender la técnica
de dibujo al óleo. El profesor le ha pedido que lleve una foto de algo
que le guste para después copiarlo en un lienzo. Una vez en clase, le
indican que tiene que dividir la foto y el lienzo en 7 columnas y 5
filas, de esa forma, cuando vaya completando el lienzo tendrá una
referencia de si está guardando bien o no la proporción. Si las columnas
y las filas de la foto son las abajo dibujadas, calcula
graficamente como deberían ser las divisiones del lienzo.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWV_g-chWzrQqIsnPr7mAuXi6pva1W1COphT5HoiLDHGH506LKOqTmIzzSnWeNAoFc1hhkdwg5-QhA8uEkohg7aoLdoi6XERSljM73uzNtPUbinvycbYpblYLRDa8FzU6JTTEs_eL2r484/s1600/12deoctubre_paso+00.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="521" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWV_g-chWzrQqIsnPr7mAuXi6pva1W1COphT5HoiLDHGH506LKOqTmIzzSnWeNAoFc1hhkdwg5-QhA8uEkohg7aoLdoi6XERSljM73uzNtPUbinvycbYpblYLRDa8FzU6JTTEs_eL2r484/s640/12deoctubre_paso+00.png" width="640" /></a><a href="http://planolineapunto.blogspot.com/2015/10/solucionteoremasejercicio-1.html">SOLUCIÓN:</a> <br />
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<br />Plano, línea, puntohttp://www.blogger.com/profile/16337620171032000437noreply@blogger.com0