Question 32
Let $A$, $B$, $C$, $D$ be fixed points on this order on a line. Let $\omega$ be a variable circle through $C$ and $D$ and suppose that it meets the perpendicular bisector of $CD$ at the points $X$ and $Y$. Let $Z$ and $T$ be the other points of intersection of $AX$ and $BY$ with $\omega$. Prove that $ZT$ passes through a fixed point which is independent of the circle $\omega$.