Školjka Two circles in a plane intersect. 
is one of the points of intersection. Starting simultaneously from two points move with constant speed, each travelling along its own circle in the same sense. The two points return to simultaneously after one revolution. Prove that there is a fixed point 
in the plane such that the two points are always equidistant from 
is one of the points of intersection. Starting simultaneously from two points move with constant speed, each travelling along its own circle in the same sense. The two points return to simultaneously after one revolution. Prove that there is a fixed point in the plane such that the two points are always equidistant from