BALKAN-SL 2018 G4

A quadrilateral $ABCD$ is inscribed in a circle $k$ where $AB$ $>$ $CD$, and $AB$ is not paralel to $CD$. Point $M$ is the intersection of diagonals $AC$ and $BD$, and the perpendicular from $M$ to $AB$ intersects the segment $AB$ at a point $E$. If $EM$ bisects the angle $CED$ prove that $AB$ is diameter of $k$. Proposed by Emil Stoyanov,Bulgaria