Question 150
Let $ABC$ be an acute triangle. Point $D$ lies on side $BC$. Let $O_B$ and $O_C$ be the circumcenters of triangles $ABD$ and $ACD$, respectively. Suppose that points $B$, $C$, $O_B$, $O_C$ lie on a circle centered at point $X$. Let $H$ be the orthocenter of triangle $ABC$. Prove that $\angle DAX = \angle DAH$.