Retos. Circunferencia, ángulos en la circunferencia

Reto 1.[br][br]Realiza una construcción para comprobar que un ángulo exterior a una circunferencia es la semidiferencia de los ángulos que intercepta.[br][img width=258,height=156]data:image/png;base64,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[/img][br][br][img width=81,height=46]data:image/png;base64,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[/img][br][br]Incluye en la vista gráfica las medidas de los arcos y su suma de manera que se pueda comprobar la igualdad.[br][br][br]
Ángulos en la circunferencia
[b]Reto 2[/b].[br][br]Dadas tres circunferencias del mismo radio, traza una circunferencia que sea tangente a las tres circunferencias.[br]¿Es única?[br]
Circunferencias tangentes
[b]Reto 3[/b].[br][br]Sea Q un punto situado en una cuerda AB de una circunferencia de centro O.[br]Traza por Q un nueva cuerda CD que sea de igual tamaño que la cuerda AB.
Cuerdas en la circunferencia

Information: Retos. Circunferencia, ángulos en la circunferencia