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D on BC, E on CA, F on AB such that BDF=CED=AFE -[INMO 2011]

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February 6, 2011
trigonometrysymmetrygeometry proposedgeometry

Problem Statement

Let D,E,FD,E,F be points on the sides BC,CA,ABBC,CA,AB respectively of a triangle ABCABC such that BD=CE=AFBD=CE=AF and ∠BDF=∠CED=∠AFE.\angle BDF=\angle CED=\angle AFE. Show that △ABC\triangle ABC is equilateral.
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