Question 16
Let $A B C$ be a triangle with $A B=A C$, and let $M$ be the midpoint of $B C$. Let $P$ be a point such that $P B\lt P C$ and $P A$ is parallel to $B C$. Let $X$ and $Y$ be points on the lines $P B$ and $P C$, respectively, so that $B$ lies on the segment $P X, C$ lies on the segment $P Y$, and $\angle P X M=\angle P Y M$. Prove that the quadrilateral $A P X Y$ is cyclic.