GeoGebra dispone de la herramienta [b]Tangentes[/b] [url=http://wiki.geogebra.org/es/Archivo:Tool_Tangents.gif][img width=32,height=32]data:image/png;base64,R0lGODlhIAAgAPcAAHFcYEQlMQsBPQQAXwAA/wAA6gAAlgAAeg4PUD4/U0lYWEtXV3qDg3d/f9/s7Jujo9vl5ff///b+/vn///v//9HV1WxubvL19U9QUEJDQ9fZ2cXHx/7//6mqqvr//aerqIWJhNjb0OHi3sqfkJVAOfJrZfWpp//g38EUFLIVFdctLWYWFuk8PP9ERP9GRv9HR/hFRf9ISP9JSfNGRqYwMP9OTv9PT/9RUf9TU+hMTP9VVf9XV/1WVv9aWaY6Ov9aWv9bW/9cXP1bW/9eXv9gYP9hYf9iYu9fX/9paf9qav9sbPlqav9tbe5nZ/9zc75XV/93d3I1Nf94eL9aWvh3d/97e/99ff9+fv+Cgv+Dg/+GhviDg/+IiP+Jif+Li/+MjP+OjpZVVf+Skv+Wlv+YmP+Zmf+bm/+fn/+goP+np/+pp/+oqP+rq/uoqP+vr/+ysv+2tv+6uv+8vLeHh3tcXP3AwFtFRf/ExP/Fxf/MzLeSkv/Pz//R0f/S0v/T0//V1f/W1v/Y2P/d3f/f3//g4P/i4v/k5P/m5v/o6P/p6fHf3//t7f/u7v/v7//w8P/x8VpVVfbq6v/29pyWlv/39/ry8v/4+P/5+f/+/v////39/fv7+/n5+fPz8/Ly8vHx8fDw8O3t7eTk5OPj493d3dra2tnZ2dLS0sPDw8DAwLu7u7m5ua2traysrKmpqaKioqCgoJycnJOTk5KSkoqKioaGhoKCgoGBgX5+fnx8fHl5eXh4eHV1dXNzc3FxcXBwcGxsbGdnZ2JiYllZWVZWVlFRUU9PT01NTUxMTEpKSklJSUVFRQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACH/C01TT0ZGSUNFOS4wFwAAAAttc09QTVNPRkZJQ0U5LjBCPKT1ACH/C01TT0ZGSUNFOS4wGAAAAAxjbVBQSkNtcDA3MTIAAAADSABzvAAsAAAAACAAIAAACP8AMwkcSLDgQEw/4hhcyJDhGyANI0a0VCOPxIsGzyDByFGgoxiCOnL8YkUkRkM3FHXAFUxYL1mlTBbM4mPBL1enTKmqhWwXKJmZEKGApMFgp1vJRslcMiVCw1fHPonsA6OSxFy2RA5pc9GTMlEc8ai4gFEXLI4swlDA6AoXRjgpGHBE5euiJRxzGnBcxeuimCoOhmnCOIuWxEUtDFEodgrjMFQSr3ARGAvYxVTENkUc9IKRQE7GWkUMlWGDRCVmCJJaxoohBAUPMCW6U2bhHxuUCprCYKGCBAoUOETSs4KGEx07mHRZmMTNwgmT7ER50kTIjBxU0MQhJGlhiBE9CD5hCsRGixIiPI5sSbOn0cUPCAYAqDMGShAcRayQkVPoEkdHgKgRQAEECFCCF2vw4ZlMP+BgBBZ0HGBAAh4ARZAf7mViAgkgiGDhQo/IcMKHDIEhBYkLHeICIigadMUXLRIUEAA7[/img][/url] que facilita el trazado de la recta tangente a una curva.[br][br]Por ejemplo, para obtener la recta tangente a una circunferencia por un punto de ella, basta con seleccionar esta herramienta, pulsando a continuación sobre la circunferencia y por último, sobre el punto[br](P).[br][br][img width=275,height=225]data:image/png;base64,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recta tangente a una circunferencia por un punto de ella forma un ángulo recto con el[br]radio trazado sobre dicho punto, que podemos medir con ayuda de la herramienta [b]Ángulo[/b] [url=http://wiki.geogebra.org/es/Archivo:Tool_Angle.gif][img width=32,height=32]data:image/png;base64,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[/img][/url].[br][br][img 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De manera análoga, podemos trazar las tangentes a una circunferencia desde un punto exterior.[br][br][img 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proceso es similar ya que basta con seleccionar la herramienta [b]Tangentes[/b], pulsando a continuación[br]sobre la circunferencia y sobre el punto P.

Podemos comprobar que la recta que une los puntos A y P es la bisectriz del ángulo formado por las dos rectas tangentes.[br][br]Como era de esperar, seguro que lo habéis descubierto, GeoGebra dispone de una herramienta para obtener la bisectriz de un ángulo.[br][br]La herramienta [b]Bisectriz[/b] [url=http://wiki.geogebra.org/es/Archivo:Tool_Angular_Bisector.gif][img width=32,height=32]data:image/png;base64,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[/img][/url] se encuentra en el bloque denominado [b]Construir[/b]. Una vez seleccionada, bastará con pulsar sobre las dos rectas para que aparezcan dibujadas.[br][br][img 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que aparecen las dos bisectrices de los dos ángulos que forman las dos rectas tangentes.