Question 100
Let $ABCD$ be an isosceles trapezoid where $BC \parallel AD$ and $AB = CD$. A circle $\omega$ passes through $B$ and $C$ and meets again the segments $AB$ and $BD$ at $X$ and $Y$, respectively. The tangent to $\omega$ at $C$ meets the ray $AD$ at $Z$. Prove that the points $X$, $Y$, and $Z$ are collinear.