As you rotate the figure (without moving the center of rotation) notice which points stay on the circle. Draw a new circle so with center at the origin that passes through point B. rotate the figure a bit. Do you see the pattern? Draw another circle with center at the origin and passing through a point on the preimage. Rotate the figure a bit. What is the pattern?
The circle has center at the point of rotation and a point from the preimage and its corresponding point on the image. In other words, if the circle centered at the point of reflection goes through point A, it will also go through point A'. If it goes through point B, it will also go through point B'.