Question 172
Let $ABC$ be a triangle with $AB = AC$ and let $M$ be the midpoint of the segment $BC$. Let $P$ be a point such that $PB \lt PC$ and $PA$ is parallel to $BC$. Furthermore, let $X$ and $Y$ be points on the lines $PB$ and $PC$, respectively, such that $B$ lies on the segment $PX$, $C$ lies on the segment $PY$, and $\angle PXM = \angle PYM$. Prove that $APXY$ is a cyclic quadrilateral.