IZhO 2016 Problem 5

A convex hexagon $ABCDEF$ is given such that $AB||DE$ , $BC||EF$ , $CD||FA$ . The point $M, N, K$ are common points of the lines $BD$ and $AE$ , $AC$ and $DF$ , $CE$ and $BF$ respectively. Prove that perpendiculars drawn from $M, N, K$ to lines $AB, CD, EF$ respectively concurrent.