MEMO 2016 I3

Let $ABC$ be an acute triangle such that $\angle BAC > 45^{\circ}$ with circumcenter $O$ . A point $P$ is chosen inside triangle $ABC$ such that $A, P, O, B$ are concyclic and the line $BP$ is perpendicular to the line $CP$ . A point $Q$ lies on the segment $BP$ such that the line $AQ$ is parallel to the line $PO$ .

Prove that $\angle QCB = \angle PCO$ .