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Mexican equal segments II

Source: Mexican Mathematical Olympiad 2004 OMM P3

July 31, 2018
geometryequal segments

Problem Statement

Let ZZ and YY be the tangency points of the incircle of the triangle ABCABC with the sides ABAB and CACA, respectively. The parallel line to YZY Z through the midpoint MM of BCBC, meets CACA in NN. Let LL be the point in CACA such that NL=ABNL = AB (and LL on the same side of NN than AA). The line MLML meets ABAB in KK. Prove that KA=NCKA = NC.
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