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Angle LNM is a right angle if ∠ALB=∠MNB

Source: Baltic Way 2002

November 13, 2010
geometry proposedgeometry

Problem Statement

Let L,ML,M and NN be points on sides AC,ABAC,AB and BCBC of triangle ABCABC, respectively, such that BLBL is the bisector of angle ABCABC and segments AN,BLAN,BL and CMCM have a common point. Prove that if ∠ALB=∠MNB\angle ALB=\angle MNB then ∠LNM=90∘\angle LNM=90^{\circ}.
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