MathNet 2015-part-02 — 191 problems (EN–VI) Question 69

Let $O$ be the circumcentre and $H$ be the orthocentre of the triangle $ABC$. Ray $AO$ intersects the circumcircle of the triangle $ABC$ in point $D$. Prove that the line $HD$ passes through the midpoint of the segment $\overline{BC}$.