Answer
The locus of the midpoint of a circle is a circle with half of the radius of the initial circle.
Work Step by Step
Recall, a midpoint is the center of the radius, so the midpoint of a radius is equal to half of the radius. In addition, recall that a locus is the curve, line, point, or plane along which the distance from a given point (it can be multiple points, but in this case we are considering the center of the circle) is constant. A constant distance away from the center of the original circle forms another circle. Thus, the locus of the midpoint of a circle is a circle with half of the radius of the initial circle.
