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slicing problem with a right angle in the end

Source: Tuymaada 2007, Problem 6

July 15, 2007
geometryperpendicular bisectorgeometry proposed

Problem Statement

Point D D is chosen on the side AB AB of triangle ABC ABC. Point L L inside the triangle ABC ABC is such that BD=LD BD=LD and ∠LAB=∠LCA=∠DCB \angle LAB=\angle LCA=\angle DCB. It is known that ∠ALD+∠ABC=180∘ \angle ALD+\angle ABC=180^\circ. Prove that ∠BLC=90∘ \angle BLC=90^\circ.
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