Problem

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

Tags: geometry, fixed, Fixed point, area of a triangle, areas



On the sides $AB$ and $BC$ of triangle $ABC$, points $M$ and $K$ are taken, respectively, so that $S_{KMC} + S_{KAC}=S_{ABC}$. Prove that all such lines $MK$ pass through one point.