Question 18
Let $ABC$ be a triangle, and let $D$ be a point on side $BC$. A line through $D$ intersects side $AB$ at $X$ and ray $AC$ at $Y$. The circumcircle of triangle $BXD$ intersects the circumcircle $\omega$ of triangle $ABC$ again at point $Z \neq B$. The lines $ZD$ and $ZY$ intersect $\omega$ again at $V$ and $W$, respectively. Prove that $AB = VW$.