Question 25
G6 (ARG). Let $ABCD$ be a convex quadrilateral with $AB$ not parallel to $CD$, let $X$ be a point inside $ABCD$ such that $\angle ADX=\angle BCX\lt 90^\circ$ and $\angle DAX=\angle CBX\lt 90^\circ$. If $Y$ is the point of intersection of the perpendicular bisectors of $AB$ and $CD$, prove that $\angle AYB=2\angle ADX$.