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Incircle cuts

Source: 2012 Indonesia Round 2 TST 2 Problem 2

March 4, 2012
geometryincentercircumcirclegeometry unsolved

Problem Statement

Let ABCABC be a triangle, and its incenter touches the sides BC,CA,ABBC,CA,AB at D,E,FD,E,F respectively. Let ADAD intersects the incircle of ABCABC at MM distinct from DD. Let DFDF intersects the circumcircle of CDMCDM at NN distinct from DD. Let CNCN intersects ABAB at GG. Prove that EC=3GFEC = 3GF.
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