Limaçon as a Pedal of a Circle

Given is a circle

, and a fixed point

. This point will be the pedal point. Let

be a random point on

, and let the line

be tangent to the circle

at point

The green point is the intersecting point of

and the perpendicular to

through

. As

moves over

, the foot of the perpendicular (the green point) will draw the pedal curve of the circle. This curve will be a

. Move the position of

: outside the circle, on the circle, or inside the circle, and see the change in the Limaçon.

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