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Concyclic points!

Source: Greek tst 2018

April 1, 2019
geometry proposedPower of Pointhomothetygeometry

Problem Statement

A triangle ABCABC is inscribed in a circle (C)(C) .Let GG the centroid of △ABC\triangle ABC . We draw the altitudes AD,BE,CFAD,BE,CF of the given triangle .Rays AGAG and GDGD meet (C) at MM and NN.Prove that points F,E,M,N F,E,M,N are concyclic.
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