HMMT 2011 S9

Let $A B C$ be a non-isosceles, non-right triangle, let $\omega$ be its circumcircle, and let $O$ be its circumcenter. Let $M$ be the midpoint of segment $B C$. Let the tangents to $\omega$ at $B$ and $C$ intersect at $X$. Prove that $\angle O A M=\angle O X A$. (Hint: use SAS similarity).