Question 87
Points $X$, $Y$, $Z$ lie on a line $k$ in this order. Let $\omega_1$, $\omega_2$, $\omega_3$ be three circles of diameters $XZ$, $XY$, $YZ$, respectively. Line $l$ passing through point $Y$ intersects $\omega_1$ at points $A$ and $D$, $\omega_2$ at $B$ and $\omega_3$ at $C$ in such manner that points $A$, $B$, $Y$, $C$, $D$ lie on $l$ in this order. Prove that $AB = CD$.
