Mongolian National Mathematical Olympiad

Let $ABCD$ be an isosceles trapezoid with $AD=BC$ and $AB\parallel CD$. Let $O$ be the intersection of the diagonals and let $M$ be the midpoint of $AD$. Circumcircle of $BCM$ intersects $AD$ again at $K$. Prove that $OK$ is parallel to $AB$.

(Proposed by B. Bat-Od)