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Rioplatense 2022 - Level 3 - Problem 2

Source:

December 6, 2022
geometry

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB<AC. Let D,E,FD,E,F be the feet of the altitudes relatives to the vertices A,B,CA,B,C, respectively. The circumcircle Γ\Gamma of AEFAEF cuts the circumcircle of ABCABC at AA and MM. Assume that BMBM is tangent to Γ\Gamma. Prove that MM, FF and DD are collinear.
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