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Limacon of Pascal

A line joins a fixed point P to a point A moving around a circle of diameter a. The curve is the locus of all points S (or S') such that PS (S') = b. If b<a/2, the curve has an inner loop; if b>a/2 the curve forms a single loop; if b=a/2, the curve is a cardioid. Moving point P changes the orientation of the these curves. Graphics 2 shows how to construct  a limacon by  rolling a circle around another  fixed circle of same diameter.