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KN + LM >= AC wanted, AK = BL, CN = BM

Source: 2005 Oral Moscow Geometry Olympiad grades 8-9 p3

October 16, 2020
geometrygeometric inequalityequal segments

Problem Statement

In triangle ABCABC, points K,PK ,P are chosen on the side ABAB so that AK=BLAK = BL, and points M,NM,N are chosen on the side BCBC so that CN=BMCN = BM. Prove that KN+LM≥ACKN + LM \ge AC.
(I. Bogdanov)
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