Question 23
Let $H$ be the orthocenter of an acute-angled $\triangle ABC$ with $\angle A \gt 60^\circ$. Let points $M$ and $N$ be on sides $AB$ and $AC$, respectively, such that $\angle HMB = 60^\circ = \angle HNC$. Let $O$ be the circumcenter of $\triangle HMN$. Let points $D$ and $A$ be on the same side of line $BC$, such that $\triangle DBC$ is regular (see Fig. 1.1). Prove that points $H$, $O$ and $D$ are collinear. (posed by Zhang Sihui)
