SHARYGIN 2015 Problem 18

Let $ABCDEF$ be a cyclic hexagon, points $K, L, M, N$ be the common points of lines $AB$ and $CD$ , $AC$ and $BD$ , $AF$ and $DE$ , $AE$ and $DF$ respectively. Prove that if three of these points are collinear then the fourth point lies on the same line.