CGMO 2006 Problem 2

Let $O$ be the intersection of the diagonals of convex quadrilateral $ABCD$ . The circumcircles of $\triangle{OAD}$ and $\triangle{OBC}$ meet at $O$ and $M$ . Line $OM$ meets the circumcircles of $\triangle{OAB}$ and $\triangle{OCD}$ at $T$ and $S$ respectively.

Prove that $M$ is the midpoint of $ST$ .