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Equal Angles at Tangent Points

Source: 2012 Baltic Way, Problem 14

November 22, 2012
geometrysimilar trianglesgeometry unsolved

Problem Statement

Given a triangle ABCABC, let its incircle touch the sides BCBC, CACA, ABAB at DD, EE, FF, respectively. Let GG be the midpoint of the segment DEDE. Prove that ∠EFC=∠GFD\angle EFC = \angle GFD.
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