Question 68
Given two triangles $PAB$ and $PCD$ such that $PA = PB$, $PC = PD$, $P$, $A$, $C$ and $B$, $P$, $D$ are collinear in this order respectively. The circle $S_1$ passing through $A$, $C$ intersects with the circle $S_2$ passing through $B$, $D$ at distinct points $X$, $Y$. Prove that the circumcenter of the triangle $PXY$ is the midpoint of the centers of $S_1$, $S_2$.
