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fixed point, S_{KMC} + S_{KAC}=S_{ABC}, area condition , two non constant points

Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p3

May 8, 2020
geometryfixedFixed pointarea of a triangleareas

Problem Statement

On the sides ABAB and BCBC of triangle ABCABC, points MM and KK are taken, respectively, so that SKMC+SKAC=SABCS_{KMC} + S_{KAC}=S_{ABC}. Prove that all such lines MKMK pass through one point.