HMMT 2024 T8

Let $P$ be a point in the interior of quadrilateral $A B C D$ such that the circumcircles of triangles $P D A, P A B$, and $P B C$ are pairwise distinct but congruent. Let the lines $A D$ and $B C$ meet at $X$. If $O$ is the circumcenter of triangle $X C D$, prove that $O P \perp A B$.