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MathNet 2017-part-03 — 176 problems (EN–VI) Question 48

Math Olympiad Vault · MathNet 2017-part-03 — 176 problems (EN–VI)

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.