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2018 PAMO Shortlist: Lenths of lines related to tangency points of incircle

Source: 2018 Pan-African Shortlist - G5

May 7, 2019
geometryTriangleParallel Linesincircle

Problem Statement

Let ABCABC be a triangle with AB≠ACAB \neq AC. The incircle of ABCABC touches the sides BCBC, CACA, ABAB at XX, YY, ZZ respectively. The line through ZZ and YY intersects BCBC extended in X′X^\prime. The lines through BB that are parallel to AXAX and ACAC intersect AX′AX^\prime in KK and LL respectively. Prove that AK=KLAK = KL.
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