La curva denominada astroide se puede construir como la envolvente de todos los segmentos de longitud r, cuyos extremos se apoyan en dos diámetros perpendiculares de una circunferencia cuyo radio es también r. [br][br][img 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realizar esta construcción, comenzamos definiendo la longitud r que puede quedar determinada por un segmento, un deslizador o por un valor numérico introducido a través de la línea de entrada.[br][br]De las opciones anteriores elegimos que r quede determinado por un segmento AB que[br]dibujamos como primer paso en la construcción.[br][br]Aprovechando los ejes de coordenadas, dibujamos el punto correspondiente al origen O, y dibujamos una circunferencia con centro en O y radio igual a la longitud del segmento AB. Para ello, utilizamos la herramienta [b]Circunferencia dado su centro y radio[/b].[br][br][img 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continuación, utilizando la herramienta [b]Intersección[/b], obtenemos los puntos de corte de la circunferencia con el eje Y. Obtendremos los puntos C y D. Creamos el segmento CD y situamos un nuevo punto P en dicho segmento.[br][br][img width=285,height=250]data:image/png;base64,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de nuevo la herramienta [b]Circunferencia dado su centro y radio[/b], dibujamos la circunferencia de centro P y radio igual a la longitud del segmento AB.[br][br]Obtenemos los puntos de intersección de esta nueva circunferencia con el eje X. Estos puntos serán E y F.[br][br][img 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el segmento PF al que cambiamos el color, por ejemplo lo dibujamos de color[br]rojo.[br][br][img 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0iN5OkXE0gYRqscicuc4HzEHsckDgCumqveafZajGsd7aQXKIdyrNGHAPTIzQBx134z1KDwM+o3GkTPclCjyBQIQSxXJwxIApngnxDJqvhOO1udDnukt/8AR90SK0UoUDn5iOfWuw07SrLStOXT7SBUtl3YjxxyST/OqfhJVTwrpyqoUCEcAYpW1uVzPl5ehDZSSWEJh03wrLbRk5wrQRqT+DZ/SrH2rXpeE0y0g95bst+ir/WtaimSZK2uuzczalbW47rb25J/Nj/Sg+HrefP266vL0Hqs05Cf98rgfpWtRQBXtLCzsU2WlrFAvcRoFz+VWKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD/2Q==[/img][br][br]Al activar el rastro del segmento PF y animar el punto P obtendremos una parte del astroide.[br]

Repitiendo el proceso para el segmento PE completaremos la representación del astroide.