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Parallel lines in a regular triangle

Source: 2020 Caucasus Mathematical Olympiad

March 16, 2020
geometryEquilateral Triangleeasy problem

Problem Statement

A regular triangle ABCABC is given. Points KK and NN lie in the segment ABAB, a point LL lies in the segment ACAC, and a point MM lies in the segment BCBC so that CL=AKCL=AK, CM=BNCM=BN, ML=KNML=KN. Prove that KL∥MNKL \parallel MN.
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