Question 36
Given a circle $\tau$, consider a quadrilateral $ABCD$ with its four sides tangent to $\tau$, with $AD$ tangent to $\tau$ at $P$ and $CD$ tangent to $\tau$ at $Q$. Let $X$ and $Y$ be the points where $BD$ cuts $\tau$, and $M$ be the midpoint of $XY$. Prove that $\angle AMP = \angle CMQ$.