Question 164
Let $C$ be a circle in the $x y$-plane with center on the $y$-axis and passing through $A=(0, a)$ and $B=(0, b)$ with $0\lt a\lt b$. Let $P$ be any other point on the circle, let $Q$ be the intersection of the line through $P$ and $A$ with the $x$-axis, and let $O=(0,0)$. Prove that $\angle B Q P=\angle B O P$.