KöMaL 2016 B4818

The intersection of diagonals $AC$ and $BD$ of a cyclic quadrilateral $ABCD$ is $M$. The angle bisectors of the angles $\angle CAD$ and $\angle ACB$ intersect the circumscribed circle of the cyclic quadrilateral $ABCD$ at points $E$ and $F$, respectively. Prove that line $EF$ is perpendicular to the angle bisector of the angle $AMD$.