Answer
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.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c853a40b-3354-40c3-acae-1c00aaf53ecd/result_image/1502531782.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021805Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=4b5fcce85623e0506716af686af48aee3d06eba6b878f4fbdce934380da7a232)
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.)