The locus is a circle with a center of the half dollar, and that passes through the centers of the penny as it rolls around the half-dollar.
Work Step by Step
As the penny remains tangent to the half-dollar $O$, $P$ and $Q$ are always col-linear. Therefore, the locus is a circle with a radius of 0,975 in. (The radius of a half-dollar is 0,6 in. and the radius of a penny is 0,375 in.)