Ejemplo 3. Siete circunferencias tangentes

[i]Realiza la construcción siguiente.[/i][br][br][i][img width=212,height=189]data:image/png;base64,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[/img][/i][br][br][i]Si las circunferencias pequeñas tienen un radio de una unidad de medida, ¿cuál es el área de la parte dibujada en rojo?[/i][br][br]Antes de iniciar la construcción de las distintas circunferencias es conveniente relacionar esta figura con otra forma conocida que ayudará para determinar los puntos de tangencia de las siete circunferencias interiores.[br]Si nos fijamos en las seis circunferencias del mismo radio que rodean a la circunferencia central, podemos observar que sus centros estarán sobre un hexágono regular, por lo que comenzaremos dibujándolo[br]utilizando para ello la herramienta [b]Polígono regular[/b][url=https://wiki.geogebra.org/es/Herramienta_de_Pol%C3%ADgono_regular][img width=24,height=24]data:image/png;base64,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[/img][/url].[br]Podemos activar la cuadrícula para considerar los puntos del lado del hexágono de manera que estén a dos unidades de distancia ya que el radio de cada una de las circunferencias es de una unidad.[br][img width=272,height=194]data:image/png;base64,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[/img][br]Sobre el hexágono dibujamos en cada uno de los vértices una circunferencia de centro cada vértice y radio una unidad. Para ello, utilizaremos la herramienta [b]Circunferencia (centro-radio)[/b][url=https://wiki.geogebra.org/es/Herramienta_de_Circunferencia_(centro-radio)][img width=24,height=24]data:image/png;base64,R0lGODlhGAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwASABIAgwAAAAAAAAAADQAALgAAPgAAPQAAOwAANwAA8gECAwECAwECAwECAwECAwECAwECAwQzEMgJQqg0z0svz5+GiaQUlh13auEKolQxbquBIAc8FbdoiQaZTucqqYYt4otUdBU7mFUEADs=[/img][/url].[br][img 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[/img][br]Para dibujar la circunferencia central determinamos su centro que será el punto medio de cualquier diagonal del hexágono.[br]Utilizamos la herramienta [b]Punto medio o centro[/b] para obtenerlo y repetimos el proceso de dibujar una circunferencia con ese centro y una unidad de radio.[br][img 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podemos ocultar el hexágono y sólo nos queda dibujar la circunferencia exterior cuyo centro es el centro del hexágono y de la que nos queda determinar un punto.[br]Para que sea tangente al resto de circunferencias,[br]trazamos una diagonal del polígono utilizando la herramienta [b]Recta[/b]. El punto de intersección con[br]cualquiera de las circunferencias exteriores será el punto que nos falta para dibujar[br]la circunferencia exterior.[br][img 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sólo queda dibujar la última de las circunferencias, ocultando a continuación la recta y si lo deseamos el punto de tangencia.
Siete circunferencias tangentes
[br][img 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[/img][br][br]Por último, para hallar el área de la parte roja basta con determinar el radio de la circunferencia exterior, sabiendo que cada una de las siete circunferencias tiene un radio igual a una unidad.[br]Podemos observar que el radio de la circunferencia exterior es 3 unidades (diámetro de una circunferencia interior más un radio).[br]Por tanto, el área de la circunferencia exterior será[br][br] [img width=104,height=22]data:image/png;base64,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[/img] [br]mientras que el área de una circunferencia interior será [br][br][img width=93,height=22]data:image/png;base64,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[/img].[br]Por tanto, el área de la zona pintada de rojo será:[br][br][img width=127,height=22]data:image/png;base64,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[/img].

Information: Ejemplo 3. Siete circunferencias tangentes