Los applets abajo ayudan a entender algunos teoremas relacionados con circunferencias.[br][br]Por ejemplo, explora las siguiente figura:
El applet arriba muestra una circunferencia con centro en A (que puedes cambiar de tamaño moviendo el punto B), una recta AC qe pasa por el centro de la circunferencia y una cuerda (EF) que es perpendicular a la recta AC.[br][br]Abajo se vuelve a presentar la misma construcción geométrica. Mide los segmentos ED y DF.
Después de medir DE y FD mueve los puntos para cambiar el tamaño de la circunferencia o la posición de la cuerda. ¿Qué notas acerca de la longitud de los segmentos DE y FD?[br][br]Utiliza tus observaciones para completar el siguiente teorema:
Si una recta que pasa por el centro de una circunferencia es perpendicular a una cuerda, entonces ...
Ahora realiza la siguiente construcción que te permitirá mostrar algunos teoremas relacionados a las tangentes a una circunferencia:[br][list=1][*]Construye una circunferencia. [icon]/images/ggb/toolbar/mode_circle2.png[/icon][/*][*]Construye un punto fuera de la circunferencia. [icon]/images/ggb/toolbar/mode_point.png[/icon][/*][*]Construye las tangentes a la circunferencia desde el punto construido en 2. [icon]/images/ggb/toolbar/mode_tangent.png[/icon][/*][*]Construye los puntos de tangencia. [icon]/images/ggb/toolbar/mode_point.png[/icon][/*][*]Construye radios a los puntos de tangencia . [icon]/images/ggb/toolbar/mode_segment.png[/icon][/*][*]Mide el ángulo formado entre una de las tangentes y el radio que va a su punto de tangencia. [icon]/images/ggb/toolbar/mode_angle.png[/icon][/*][*]Mide la longitud de los segmentos que van del punto construido en 2 y cada punto de tangencia.[/*][/list]Tu construcción debe verse algo así:[br][center][img]data:image/png;base64,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[/img][/center]
Mueve los puntos para cambiar el tamaño de la circunferencia y la posición del punto común de las tangentes. ¿Qué notas sobre el ángulo formado entre una tangente y el radio al punto de tangencia? ¿Qué notas sobre la longitud de los segmentos que van del punto común a los puntos de tangencia?[br][br]Completa los siguientes teoremas:
Una recta tangente a una circunferencia y el radio construido al punto de tangencia ...
Dos segmentos que van desde puntos de tangencia diferentes a un punto en común ...
Construye un ángulo central y uno inscrito que intersequen a la circunferencia en los mismos puntos:[br][list=1][*]Construye una circunferencia. [icon]/images/ggb/toolbar/mode_circle2.png[/icon][/*][*]Construye dos puntos adicionales sobre la circunferencia (en total habrá tres puntos sobre la circunferencia). [icon]/images/ggb/toolbar/mode_point.png[/icon][/*][*]Construye una semirrecta que parta del centro y pase por uno de los puntos. Después construye otra semirrecta que parta del centro y pase por otro de los puntos. Con esto habrás formado un ángulo central. [icon]/images/ggb/toolbar/mode_ray.png[/icon][/*][*]Construye una semirrectas que partan del tercer punto hacia los puntos sobre la circunferencia que usaste para formar el ángulo en 3. El ángulo que formaste ahora es un ángulo inscrito. [icon]/images/ggb/toolbar/mode_ray.png[/icon][/*][*]Mide el ángulo central y el ángulo inscrito. [icon]/images/ggb/toolbar/mode_angle.png[/icon][/*][/list]Tu construcción debería verse más o menos así:[br][center][img]data:image/png;base64,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[/img][/center]
Mueve los puntos para cambiar el tamaño de la circunferencia y la posición de los puntos sobre la circunferencia. ¿Qué notas acerca de la medida de los ángulos?[br][br]Utiliza tus observaciones para completar el siguiente teorema:
La medida de un ángulo inscrito es ...