[i]Sea A un punto interior de una circunferencia c. [/i][i]Halla el lugar geométrico de los centros de las circunferencias que pasan por el punto A que son tangentes a la circunferencia c.[/i][br][br][i]¿Qué ocurre cuando el punto A es exterior a la circunferencia?[/i][br][br]Después de trazar la circunferencia c, definimos un punto B perteneciente a c y un punto A interior.[br][br]Para dibujar la circunferencia que pasa por el punto A, que es tangente en el punto B a la circunferencia c, necesitamos encontrar su centro. [br][br]El centro, que llamamos P, será el punto de intersección de la mediatriz del segmento AB con el segmento OB siendo O el centro de la circunferencia c.[br][br]Para trazar el lugar geométrico debemos seleccionar la correspondiente herramienta, y señalar a continuación  el punto P  y el punto B.[br][br][img 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[/img][br][br]El lugar geométrico representa una elipse cuyos focos son los puntos O y A.[br][br]Para responder a la última cuestión bastará con mover el punto A para que cumpla la condición de exterior a la circunferencia. En este caso, la cónica cambiará y el lugar geométrico será una hipérbola.[br][br]