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MMO 208 Moscow MO 1952 angle of touchpoints with incircle is acute

Source:

August 7, 2019
geometryacuteanglesincircle

Problem Statement

The circle is inscribed in △ABC\vartriangle ABC. Let L,M,NL, M, N be the tangent points of the circle with sides AB,AC,BCAB, AC, BC, respectively. Prove that ∠MLN\angle MLN is always an acute angle.
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