Descubierto por el matemático francés [i]Joseph Diaz Gergonne [/i](1771-1859), se obtiene como punto de intersección de las rectas que unen los vértices del triángulo con los puntos de tangencia de la circunferencia inscrita.[br]Una vez dibujado el triángulo ABC, dibujamos la circunferencia inscrita, para lo que necesitamos el incentro que es el punto de corte de las bisectrices.[br]Por tanto, seleccionamos la herramienta [b]Bisectriz[/b] [img width=24,height=24]data:image/png;base64,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[/img], marcando a continuación los tres vértices[br]ABC para obtener la bisectriz en B.[br][img 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el proceso para los vértices BCA y CAB, obteniendo el punto de intersección que será el incentro.[br][br][img 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obtener la circunferencia inscrita necesitamos los puntos de tangencia con cada lado. Hay que tener en cuenta que en una circunferencia la recta tangente por un punto es perpendicular al radio.[br][br][img width=258,height=183]data:image/png;base64,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[/img][br][br]Para obtener los puntos de tangencia trazamos las rectas perpendiculares a cada uno de los lados por el incentro.[br][br][img 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[/img][br][br]Hemos cambiado el aspecto de estas rectas que aparecen con trazo discontinuo y hemos obtenido los puntos de intersección de cada una de ellas con su lado respectivo.[br]A continuación ocultamos todas las rectas, teniendo una figura similar a la siguiente en la que I es el[br]incentro y H, J y K los puntos de tangencia.[br][br][img width=416,height=194]data:image/png;base64,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punto de Gergonne es el punto de intersección de las rectas que unen cada vértice con el punto de[br]tangencia de la circunferencia inscrita en el lado opuesto, por lo que trazamos las rectas AH, BJ y CK.[br][br][img 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BRRRQAUUUUAFFFFACVmT6BaSSme38yyuD1ltX8sn6jo34itSigDH365p4/eRxapEP4o8RTfkflb8xR/wkcHfT9UB7j7FJx+QrXIzRj3oAMCloooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAMjwtx4ctFPVAy/kxFa9FFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAH//Z[/img][br]El punto L de intersección de estas rectas, al que hemos cambiado su aspecto, es el punto de Gergonne.[br]