Let L,M and N be points on sides AC,AB and BC of triangle ABC, respectively, such that BL is the bisector of angle ABC and segments AN,BL and CM have a common point. Prove that if ∠ALB=∠MNB then ∠LNM=90∘.
Source: Baltic Way 2002
Tags: geometry proposed, geometry
Let L,M and N be points on sides AC,AB and BC of triangle ABC, respectively, such that BL is the bisector of angle ABC and segments AN,BL and CM have a common point. Prove that if ∠ALB=∠MNB then ∠LNM=90∘.