A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circle and t be the angle that L makes with the positive x-axis.  Parametric equations of the path traced out by P are  x(t) = 3r cos t + b cos 3t   and   y(t) = 3r sin t + b sin 3t Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius b centered at the center of the epitrochoid.

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