US-TST 2009 Problem 2

Let $ABC$ be an acute triangle. Point $D$ lies on side $BC$ . Let $O_B, O_C$ be the circumcenters of triangles $ABD$ and $ACD$ , respectively. Suppose that the points $B, C, O_B, O_C$ lies on a circle centered at $X$ . Let $H$ be the orthocenter of triangle $ABC$ . Prove that $\angle{DAX} = \angle{DAH}$ .

Zuming Feng.