Question 126
Let $A B C$ be an acute triangle with $A B \lt A C$. Let $J$ be the center of the $A$-excircle of $A B C$. Let $D$ be the projection of $J$ on line $B C$. The internal bisectors of angles $B D J$ and $J D C$ intersect lines $B J$ and $J C$ at $X$ and $Y$, respectively. Segments $X Y$ and $J D$ intersect at $P$. Let $Q$ be the projection of $A$ on line $B C$. Prove that the internal angle bisector of $Q A P$ is perpendicular to line $X Y$.