MathNet 2017-part-04 — 176 problems (EN–VI) Question 141

Let $ABC$ be a triangle such that $AB \neq AC$, let $G$ be its centroid, and let $H$ be its orthocenter. Let $D$ be the orthogonal projection of $A$ on the line $BC$, and let $M$ be the midpoint of the side $BC$. The circle $ABC$ crosses the ray $MH$ emanating from $M$ at $P$, and the ray $DG$ emanating from $D$ at $Q$, outside the segment $DG$. Show that the lines $DP$ and $MQ$ meet on the circle $ABC$.

BMO 2017 Shortlist