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Prove that F is the midpoint of AB [Slovenia 2010]

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November 14, 2010
trigonometrygeometryangle bisectorgeometry proposed

Problem Statement

Let ABCABC be an isosceles triangle with apex at C.C. Let DD and EE be two points on the sides ACAC and BCBC such that the angle bisectors ∠DEB\angle DEB and ∠ADE\angle ADE meet at F,F, which lies on segment AB.AB. Prove that FF is the midpoint of AB.AB.
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