Question 141
Let $P$ be a point in the interior of quadrilateral $ABCD$ such that the circumcircles of triangles $PDA$, $PAB$, and $PBC$ are pairwise distinct but congruent. Let the lines $AD$ and $BC$ meet at $X$. If $O$ is the circumcenter of triangle $XCD$, prove that $OP \perp AB$.