Question 48
Let $ABC$ be a triangle with $AB \lt AC$, inscribed in a circle $c$ of center $O$. Let $G$ be its barycenter and $D, E, F$ the foot of the altitudes from $A, B, C$, respectively. If the rays $AG, GD$ intersect $c$ at $M, N$ respectively, prove that the points $F, E, M, N$ are cocyclic.