[i]Sea c una circunferencia de centro O, A un punto en la circunferencia y P un punto[br]interior a la circunferencia.[/i][br][br][i]Traza la circunferencia que pasa por el punto P y es tangente a la circunferencia c en el punto A.[/i][br][br]Dibujamos la circunferencia y cambiamos de nombre al centro, dibujando un nuevo punto en la circunferencia que sea distinto del que hemos utilizado anteriormente para crearla. Este nuevo punto será A.[br]También dibujamos un nuevo punto P exterior a la circunferencia.[br][img width=247,height=178]data:image/png;base64,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[/img].[br]Para trazar la circunferencia pedida necesitamos encontrar su centro, para lo que aplicaremos los datos que tenemos.[br]Como la circunferencia que buscamos es tangente en A, significa que pasa por A y como también pasa por P, el centro estará a la misma distancia de esos dos puntos, por lo que estará en la mediatriz del[br]segmento AP.[br]Trazamos la mediatriz del segmento AP.[br][br][img 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recordamos la última actividad propuesta en el tema 1, los centros de dos circunferencias tangentes están en la misma recta que además pasa por el punto de tangencia, por lo que trazamos la recta que[br]pasa por O y por A.[br][br][img width=207,height=146]data:image/png;base64,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[/img][br][br]El centro estará en las dos rectas, por lo que será el punto de intersección que determinamos utilizando la herramienta [b]Intersección[/b].[br]Ya sólo queda dibujar la circunferencia que tiene por centro este punto y que pasa por A o por P.