KöMaL 2026 B5549

Scalene triangle $ABC$ is given. Let $O$ denote the circumcenter of the triangle. Let $P$ denote the intersection point, other than $O$, of the circle with diameter $AO$ and circle $BCO$. Similarly, let $Q$ denote the second intersection point of the circle with diameter $BO$ and circle $CAO$. Finally, let $R$ denote the second intersection point of the circle with diameter $CO$ and circle $ABO$. Prove that points $P$, $Q$, $R$ and $O$ are concyclic.