Question 36
Given a parallelogram $ABCD$. The line perpendicular to $AC$ passing through $C$ and the line perpendicular to $BD$ passing through $A$ intersect at point $P$. The circle centered at point $P$ and radius $PC$ intersects the line $BC$ at point $X$ ($X \neq C$) and the line $DC$ at point $Y$ ($Y \neq C$). Prove that the line $AX$ passes through the point $Y$.