Question 15
Let $\triangle ABC$ be an acute triangle with $AB \gt AC$. Let $P$ be the foot of the altitude from $C$ to $AB$ and let $Q$ be the foot of the altitude from $B$ to $AC$. Let $X$ be the intersection of $PQ$ and $BC$. Let the intersection of the circumcircles of triangle $\triangle AXC$ and triangle $\triangle PQC$ be distinct points: $C$ and $Y$. Prove that $PY$ bisects $AX$.