RU-ALLRUSSIAN 2017 Problem 92

$ABCD$ is an isosceles trapezoid with $BC || AD$ . A circle $\omega$ passing through $B$ and $C$ intersects the side $AB$ and the diagonal $BD$ at points $X$ and $Y$ respectively. Tangent to $\omega$ at $C$ intersects the line $AD$ at $Z$ . Prove that the points $X$ , $Y$ , and $Z$ are collinear.