Question 22
(USS 3) IMO3. There are two circles in the plane. Let a point $A$ be one of the points of intersection of these circles. Two points begin moving simultaneously with constant speeds from the point $A$, each point along its own circle. The two points return to the point $A$ at the same time. Prove that there is a point $P$ in the plane such that at every moment of time the distances from the point $P$ to the moving points are equal.