CWMO 2010 Problem 2

$AB$ is a diameter of a circle with center $O$ . Let $C$ and $D$ be two different points on the circle on the same side of $AB$ , and the lines tangent to the circle at points $C$ and $D$ meet at $E$ . Segments $AD$ and $BC$ meet at $F$ . Lines $EF$ and $AB$ meet at $M$ . Prove that $E,C,M$ and $D$ are concyclic.