Go Geometry Problem Problem 329. Triangle, Altitudes, Circle, Diameter, Concyclic points

The figure shows an acute triangle ABC with altitudes AD and CG. The circle with diameter BC intersects AD at E and F, and the circle with diameter AB intersects CG at M and N. Prove that the points F, M, E, and N are concyclic (lie on a same circle).

Triangle, Altitudes, DIameter, Circle, Concyclic
 

 

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