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Geometry Problem 728: Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency. Level: High School, Honors Geometry, College, Mathematics Education

The diagram shows a triangle ABC with the altitude BD. E is on BD and F is on BD extended such that DE = DF. The circumcircle of triangle AEF meets AB and AC at N and G, respectively. The circumcircle of triangle CEF meets BC and AC at M and H, respectively. Prove that BF, MH, and NG are concurrent.
 

 Triangle, Circle, Perpendicular, Concurrent
 

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