Question 149
A quadrilateral $ABCD$ is inscribed in a circle $k$, where $AB \gt CD$ and $AB$ is not parallel to $CD$. Point $M$ is the intersection of the diagonals $AC$ and $BD$ and the perpendicular from $M$ to $AB$ intersects the segment $AB$ at the point $E$. If $EM$ bisects the angle $CED$, prove that $AB$ is a diameter of the circle $k$.