Question 125
Convex quadrilateral $ABCD$ with $BC = CD$ is inscribed in circle $\Omega$; the diagonals of $ABCD$ meet at $X$. Suppose $AD \lt AB$, the circumcircle of triangle $BCX$ intersects segment $AB$ at a point $Y \neq B$, and ray $\overrightarrow{CY}$ meets $\Omega$ again at a point $Z \neq C$. Prove that ray $\overrightarrow{DY}$ bisects angle $ZDB$.