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line passes through the incentre

Source: All-Russian 2007

May 4, 2007
geometryincentergeometry unsolved

Problem Statement

A line, which passes through the incentre II of the triangle ABCABC, meets its sides ABAB and BCBC at the points MM and NN respectively. The triangle BMNBMN is acute. The points K,LK,L are chosen on the side ACAC such that ∠ILA=∠IMB\angle ILA=\angle IMB and ∠KC=∠INB\angle KC=\angle INB. Prove that AM+KL+CN=ACAM+KL+CN=AC. S. Berlov
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