Programm on Mathematica please. Thanks for the future help.

A cardioid is the curve described by a fixed point on the perimeter of a circle rolling around another circle of the same radius. The cardioid can be obtained also as the envelope of circles. Consider a given circle. Draw circles with their center on the given circle and all circles passing through a chosen point on the initial circle. The envelope of all those circles is a cardioid. Suggestion. You might find the Circlell and CirclePoints[] commands useful. A cardioid is the curve described by a fixed point on the perimeter of a circle rolling around another circle of the same radius. The cardioid can be obtained also as the envelope of circles. Consider a given circle. Draw circles with their center on the given circle and all circles passing through a chosen point on the initial circle. The envelope of all those circles is a cardioid. Suggestion. You might find the Circlell and CirclePoints[] commands useful