Let [math]P[/math] be a point and [math]c[/math] be a circle whose center is not [math]P[/math]. For any point on the circle [math]c[/math] we construct another circle with center this point and passing through [math]P[/math].[br][b]The envelope of the circles with centers on [math]c [/math]and passing through [math]P[/math] is a Limaçon.[/b][br][list][br][*]Drag the slider, or click the Animation ON/OFF button to construct the circles.[br][*]Drag point [math]P[/math]: outside the circle [math]c[/math], on the circle, or inside the circle, to see the changes in the Limaçon. [br][*]For what position of [math]P[/math] the limaçon is a dimpled,with cusp (a cardioid) or a limaçon with a loop?[br][/list]