Ejemplo 5. Rectas tangentes a una circunferencia por un punto exterior

[i]Sea P un punto exterior a una circunferencia de centro O. Traza las rectas tangentes a la circunferencia por el punto P.[/i][br][i]¿Qué propiedades cumplen las dos tangentes?[/i][br][br]Comenzamos dibujando una circunferencia y un punto exterior P, cambiando el nombre al centro para que sea O.[br][img width=252,height=175]data:image/png;base64,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[/img][br]Utilizando la herramienta [b]Tangentes[/b] obtendremos de forma directa las dos rectas tangentes a la circunferencia por el punto P.[br][br][img 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observar la figura para hacer la construcción utilizando las relaciones matemáticas entre las rectas tangentes y la circunferencia.[br]La recta que une P con el centro es la bisectriz del ángulo que forman las dos rectas tangentes.[br]Podemos hallar el centro del segmento OP, dibujando a continuación la circunferencia que tiene ese centro y pasa por P.[br][img width=308,height=205]data:image/png;base64,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puntos de intersección de estas dos circunferencias son los puntos de tangencia que hallaremos con la herramienta [b]Intersección[/b].[br][br][img width=297,height=208]data:image/png;base64,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rectas tangentes se obtendrán con la herramienta [b]Recta[/b] dibujando las que pasan por P y cada uno de estos puntos de intersección.
Rectas tangentes desde un punto exterior a unq circunferencia

Information: Ejemplo 5. Rectas tangentes a una circunferencia por un punto exterior