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BALTIC-WAY 2012 Problem 14

    Given a triangle ABCA B C, let its incircle touch the sides BC,CA,ABB C, C A, A B at D,E,FD, E, F, respectively. Let GG be the midpoint of the segment DED E. Prove that ∠EFC=\angle E F C= ∠GFD\angle G F D.

    Dataset text NuminaMath olympiads. Quoted with source.

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