Question 8
Let $ABC$ be an acute-angled triangle. A circle passing through its vertex $B$ and its circumcenter $O$ intersects the sides $BC$ and $BA$ at points $P \neq B$ and $Q \neq B$ respectively. Prove that the orthocenter of triangle $POQ$ lies on line $AC$. (T. Emelyanova, L. Emelyanov)