Question 33
Let $ABC$ 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 $BC$. Let the circumcircle of triangle $AOM$ intersect $\omega$ again at $D$. If $H$ is the orthocenter of triangle $ABC$, prove that $\angle DAH = \angle MAO$.