The locus is a circle inside of the larger circle.
Work Step by Step
Recall, a locus is equidistant from the circle no matter where you are. Therefore, first construct the original circle. Then, draw a circle (which is red in the diagram) that is equidistant from the points. There is only one circle that satisfies this requirement, for the book specifies that it wants the circle to be the midpoint of the radius of the other circle, meaning that it must be 4 cm away from the other circle.