Question 150
Let $J H I Z$ be a rectangle, and let $A$ and $C$ be points on sides $Z I$ and $Z J$, respectively. The perpendicular from $A$ to $C H$ intersects line $H I$ in $X$, and the perpendicular from $C$ to $A H$ intersects line $H J$ in $Y$. Prove that $X, Y$ and $Z$ are collinear (lie on the same line).