Antonio Vallecillos: Caso 10A (PRC) de Apolonio

Caso 10A (Caso general). Hasta cuatro soluciones:

<div style='clear: both;'></div> </div> <div class='post-footer'> <div class='post-footer-line post-footer-line-1'> <span class='post-author vcard'> Posted by <span class='fn' itemprop='author' itemscope='itemscope' itemtype='http://schema.org/Person'> <span itemprop='name'>Antonio Vallecillos</span> </span> </span> <span class='post-timestamp'> at <meta content='http://antoniovallecillos.blogspot.com/2013/02/estudio-sistematico-de-tangencias-caso.html' itemprop='url'/> <a class='timestamp-link' href='http://antoniovallecillos.blogspot.com/2013/02/estudio-sistematico-de-tangencias-caso.html' rel='bookmark' title='permanent link'><abbr class='published' itemprop='datePublished' title='2013-02-13T23:07:00+01:00'>23:07</abbr></a> </span> <span class='post-comment-link'> </span> <span class='post-icons'> <span class='item-action'> <a href='https://draft.blogger.com/email-post.g?blogID=1628286063038102165&postID=4972371467014105631' title='Enviar entrada por correo electrónico'> <img alt='' 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href='http://antoniovallecillos.blogspot.com/search/label/mOway'>mOway</a> <span dir='ltr'>(8)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/%C3%93ptica'>Óptica</a> <span dir='ltr'>(4)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/p5.js'>p5.js</a> <span dir='ltr'>(22)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/p5.play'>p5.play</a> <span dir='ltr'>(1)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Photoshop'>Photoshop</a> <span dir='ltr'>(1)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Processing'>Processing</a> <span dir='ltr'>(3)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Programaci%C3%B3n'>Programación</a> <span dir='ltr'>(88)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Qu%C3%ADmica'>Química</a> <span dir='ltr'>(2)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Rob%C3%B3tica'>Robótica</a> <span dir='ltr'>(63)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Scratch'>Scratch</a> <span dir='ltr'>(8)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/SketchUp'>SketchUp</a> <span dir='ltr'>(54)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Tecnolog%C3%ADa'>Tecnología</a> <span dir='ltr'>(178)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Tel%C3%A9fono%20M%C3%B3vil'>Teléfono Móvil</a> <span dir='ltr'>(11)</span> </li> <li> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/V%C3%ADdeo'>Vídeo</a> <span dir='ltr'>(122)</span> </li> </ul> <div class='clear'></div> </div> </div><div class='widget Label' data-version='1' id='Label1'> <h2>Dibujo Técnico</h2> <div class='widget-content cloud-label-widget-content'> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Abatimiento'>Abatimiento</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Acotaci%C3%B3n'>Acotación</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Afinidad'>Afinidad</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/%C3%81ngulos'>Ángulos</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Apolonio'>Apolonio</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Apotema'>Apotema</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Arco%20Capaz'>Arco Capaz</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/%C3%81rea'>Área</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/As%C3%ADntotas'>Asíntotas</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Baricentro'>Baricentro</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Bisectriz'>Bisectriz</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cambio%20de%20Plano'>Cambio de Plano</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Centro%20Radical'>Centro Radical</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cicloide'>Cicloide</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cilindro'>Cilindro</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circuncentro'>Circuncentro</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circunferencia'>Circunferencia</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circunferencia%20de%20Autoinversi%C3%B3n'>Circunferencia de Autoinversión</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circunferencia%20Equipotencial'>Circunferencia Equipotencial</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circunferencia%20Focal'>Circunferencia Focal</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Circunferencia%20Principal'>Circunferencia Principal</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Coeficiente%20de%20Reducci%C3%B3n'>Coeficiente de Reducción</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cono'>Cono</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Corte'>Corte</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cuadrado'>Cuadrado</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cuadril%C3%A1tero'>Cuadrilátero</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Cubierta'>Cubierta</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Curvas%20C%C3%ADclicas'>Curvas Cíclicas</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Curvas%20C%C3%B3nicas'>Curvas Cónicas</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Curvas%20T%C3%A9cnicas'>Curvas Técnicas</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Desarrollos'>Desarrollos</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Di%C3%A1metros%20Conjugados'>Diámetros Conjugados</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Distancias'>Distancias</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Dodecaedro'>Dodecaedro</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Eje%20Radical'>Eje Radical</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Elipse'>Elipse</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Enlaces'>Enlaces</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Epicicloide'>Epicicloide</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Equivalencia'>Equivalencia</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Escala'>Escala</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Esfera'>Esfera</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Espiral'>Espiral</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Espiral%20%C3%81urea'>Espiral Áurea</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Espiral%20de%20Fibonacci'>Espiral de Fibonacci</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Exincentro'>Exincentro</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Generatriz'>Generatriz</a> </span> <span class='label-size label-size-5'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Geometr%C3%ADa%20Descriptiva'>Geometría Descriptiva</a> </span> <span class='label-size label-size-5'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Geometr%C3%ADa%20Plana'>Geometría Plana</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Giro'>Giro</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Hept%C3%A1gono'>Heptágono</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Hexaedro'>Hexaedro</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Hex%C3%A1gono'>Hexágono</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Hip%C3%A9rbola'>Hipérbola</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Hipocicloide'>Hipocicloide</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Homolog%C3%ADa'>Homología</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Homotecia'>Homotecia</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Icosaedro'>Icosaedro</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Idea%20Feliz'>Idea Feliz</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Igualdad'>Igualdad</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Incentro'>Incentro</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Intersecciones'>Intersecciones</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Inversi%C3%B3n'>Inversión</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Mapa%20Conceptual'>Mapa Conceptual</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Mediana'>Mediana</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Mediatriz'>Mediatriz</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Normalizaci%C3%B3n'>Normalización</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Octaedro'>Octaedro</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Oct%C3%B3gono'>Octógono</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Ortocentro'>Ortocentro</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Par%C3%A1bola'>Parábola</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Paralelismo'>Paralelismo</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pendiente'>Pendiente</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pent%C3%A1gono'>Pentágono</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Perpendicularidad'>Perpendicularidad</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Perspectiva%20Caballera'>Perspectiva Caballera</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pertenencia'>Pertenencia</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pieza'>Pieza</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pir%C3%A1mide'>Pirámide</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pit%C3%A1goras'>Pitágoras</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Plano%20Bisector'>Plano Bisector</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Poliedros%20Regulares'>Poliedros Regulares</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pol%C3%ADgono%20Estrellado'>Polígono Estrellado</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Pol%C3%ADgonos'>Polígonos</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Potencia'>Potencia</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Prisma'>Prisma</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Puntos%20Rectas%20y%20Planos'>Puntos Rectas y Planos</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Rect%C3%A1ngulo'>Rectángulo</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Rect%C3%A1ngulo%20%C3%81ureo'>Rectángulo Áureo</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Rombo'>Rombo</a> </span> <span class='label-size label-size-1'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Romboide'>Romboide</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Secciones%20Planas'>Secciones Planas</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Semejanza'>Semejanza</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Simetr%C3%ADa'>Simetría</a> </span> <span class='label-size label-size-2'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Sistema%20Acotado'>Sistema Acotado</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Sistema%20Axonom%C3%A9trico'>Sistema Axonométrico</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Sistema%20C%C3%B3nico'>Sistema Cónico</a> </span> <span class='label-size label-size-5'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Sistema%20Di%C3%A9drico'>Sistema Diédrico</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Sistema%20Di%C3%A9drico%20Directo'>Sistema Diédrico Directo</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Superficies'>Superficies</a> </span> <span class='label-size label-size-4'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Tangencias'>Tangencias</a> </span> <span class='label-size label-size-3'> <a dir='ltr' href='http://antoniovallecillos.blogspot.com/search/label/Tarjeta'>Tarjeta</a> </span> <span class='label-size label-size-2'> <a dir='ltr' 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<div class='clear'></div> </div> </div><div class='widget AdSense' data-version='1' id='AdSense1'> <div class='widget-content'> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-1990276357130333" data-ad-host="ca-host-pub-1556223355139109" data-ad-slot="9638007949" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <div class='clear'></div> </div> </div><div class='widget Text' data-version='1' id='Text1'> <h2 class='title'>Enlaces</h2> <div class='widget-content'> DIBUJO TÉCNICO:<br /><a href="http://www.trazoide.com/">Trazoide</a><br /><a href="http://www.laslaminas.es/">laslaminas.es</a><br /><a href="http://dibutic.blogspot.com.es/">Dibujoymates</a><br /><br />TECNOLOGÍA:<br /><a href="http://tecnokent.wordpress.com/">TecnoKent</a><br /><a href="http://fermoya.com/">Tecnología ESO y Bachillerato</a><br /><a href="https://github.com/ElCableAmarillo">El Cable Amarillo</a><br /><a href="http://www.practicasconarduino.com/">EduBásica</a><br /><br />PROGRAMACIÓN Y ROBÓTICA:<br /><a href="http://scratch.mit.edu/">Scratch</a><br /><a href="http://arduino.cc/">Arduino</a><br /><a href="http://moway-robot.com/">mOway</a><br /><a href="https://processing.org/">Processing</a><br /><a href="https://p5js.org/">p5.js</a><br /><a href="http://fritzing.org/home/">Fritzing</a><br /><br />FÍSICA Y QUÍMICA:<br /><a href="http://pinpanplot.blogspot.com/">PinPanPlot</a><br /><a href="http://fq-experimentos.blogspot.com.es/">fq-experimentos</a><br /><br />CIENCIA:<br /><a href="http://naukas.com/">Naukas</a><br /><a href="http://eltamiz.com/">El Tamiz</a><br /><a href="http://www.ciencia-explicada.com/">Ciencia explicada</a><br /><a href="http://www.youtube.com/user/minutephysics">Minute Physics</a><br /><a href="http://radioskylab.es/">Radio Skylab (podcast)</a><br /><a href="http://www.rtve.es/alacarta/audios/a-hombros-de-gigantes/">A hombros de gigantes (podcast)</a><br /><a href="http://www.eitb.eus/es/radio/radio-euskadi/programas/la-mecanica-del-caracol/">La mecánica del caracol (podcast)</a><br /><a href="https://molasaber.org/">molaSABER</a><br /><a href="http://danielmarin.naukas.com/">Eureka</a><br /><br />EDUCACIÓN:<br /><a href="http://www.educacontic.es/">educ@conTIC</a><br /><a href="http://docente2punto0.blogspot.com.ar/">docente2punto0</a><br /> </div> <div class='clear'></div> </div><div class='widget Text' data-version='1' id='Text2'> <h2 class='title'>Mis blogs</h2> <div class='widget-content'> <div><a href="http://fotovallegrafia.blogspot.com.es/">Fotovallegrafía</a></div><div><a href="http://pasajeshistoria.blogspot.com.es/">Pasajes de la Historia</a></div><div><a href="http://antoniovallecillos.blogspot.com.es/">Antonio Vallecillos</a></div><a href="https://mecavolt.blogspot.com/">Mecavolt</a> </div> <div class='clear'></div> 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2013/02/13

Caso 10A (PRC) de Apolonio