Cardiod via perpendiculars to tangent lines

Study what's going on in this construction:[br][list][*]Point A is the center of a circle of fixed radius.[/*][*]Point B is a point revolving along the circle[/*][*]A line is drawn perpendicular to the circle at point B.[/*][*]A perpendicular segment is drawn from fixed point C on the circle to the tangent line, meeting the tangent line at point D.[/*][/list]Let your eye follow point D, observing what shape it traces.[br][br]The "step" slider walks through the steps of this process.[br]With a little playing around, it should become evident what any other sliders/toggles do.
Slider "n" determines the number of points evenly distributed around a circle.[br]Slider "m" cycles through those points, drawing a cord originating from the nth point, labeled "A."[br]As point A increments one position at a time, slider "coeff" determines the number of positions that endpoint "B" jumps.[br]With a little playing around, it should become evident what any other sliders/toggles do.

Información: Cardiod via perpendiculars to tangent lines