MathNet 2024-part-03 — 168 problems (EN–VI) Question 124

Let $O$ be the center of the circumcircle of an acute-angled triangle $ABC$. Let $CD$ be an altitude of the triangle, and let $M$ be a point on the segment $CD$. Let $E$ and $F$ be feet of perpendiculars from $M$ to $BC$ and $AC$, respectively. Let $G$ be the point symmetric to $C$ with respect to the line $EF$. Prove that the points $M, O, G$, and $D$ are concyclic.

(Khulan Tumenbayar)