Question 125
Let $ABC$ be an acute-angled triangle with $\Varangle BAC \gt 45^{\circ}$ and with circumcentre $O$. The point $P$ lies in its interior such that the points $A, P, O, B$ lie on a circle and $BP$ is perpendicular to $CP$. The point $Q$ lies on the segment $BP$ such that $AQ$ is parallel to $PO$.
Prove that $\Varangle QCB = \Varangle PCO$.
Prove that $\Varangle QCB = \Varangle PCO$.