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angle chasing candidate, right angle wanted, equal angles given

Source: Dutch IMO TST2 2012 p4

August 6, 2019
geometryright angleequal anglesAngle Chasing

Problem Statement

Let △ABC\vartriangle ABC be a triangle. The angle bisector of ∠CAB\angle CAB intersectsBC BC at LL. On the interior of line segments ACAC and ABAB, two points, MM and NN, respectively, are chosen in such a way that the lines AL,BMAL, BM and CNCN are concurrent, and such that ∠AMN=∠ALB\angle AMN = \angle ALB. Prove that ∠NML=90o\angle NML = 90^o.
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