Question 126
Let $ABCD$ be a convex quadrilateral. Let $O$ be the intersection of $AC$ and $BD$. Let $O$ and $M$ be the intersections of the circumcircle of $\triangle OAD$ with the circumcircle of $\triangle OBC$. Let $T$ and $S$ be the intersections of $OM$ with the circumcircle of $\triangle OAB$ and $\triangle OCD$ respectively. Prove that $M$ is the midpoint of $TS$.