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Izho 2016P5

Source: Izho 2016 P5

January 16, 2016

Problem Statement

A convex hexagon ABCDEFABCDEF is given such that AB∣∣DEAB||DE, BC∣∣EFBC||EF, CD∣∣FACD||FA. The point M,N,KM, N, K are common points of the lines BDBD and AEAE, ACAC and DFDF, CECE and BFBF respectively. Prove that perpendiculars drawn from M,N,KM, N, K to lines AB,CD,EFAB, CD, EF respectively concurrent.
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