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It seems difficult ! harmonic ratios?

Source: Greek Olympiad - 2006 , Senior

February 25, 2006
ratioIMO Shortlistgeometry proposedgeometry

Problem Statement

Let a triangle ABCABC and the cevians AL,BN,CMAL, BN , CM such that ALAL is the bisector of angle AA. If ∠ALB=∠ANM\angle ALB = \angle ANM, prove that ∠MNL=90\angle MNL = 90.
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