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China Northern Mathematical Olympiad 2017, Problem 3

Source: China Northern Mathematical Olympiad 2017

July 29, 2017
geometrySpiral SimilarityTriangle

Problem Statement

Let DD be the midpoint of side BCBC of triangle ABCABC. Let E,FE, F be points on sides AB,ACAB, AC respectively such that DE=DFDE = DF. Prove that AE+AF=BE+CF  ⟺  ∠EDF=∠BACAE + AF = BE + CF \iff \angle EDF = \angle BAC.
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