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Metric relation in a hexagon

Source: Tuymaada 2013, Day 1, Problem 2 Juniors

July 20, 2013
geometryvectorratiogeometry proposed

Problem Statement

ABCDEFABCDEF is a convex hexagon, such that in it AC∥DFAC \parallel DF, BD∥AEBD \parallel AE and CE∥BFCE \parallel BF. Prove that AB2+CD2+EF2=BC2+DE2+AF2.AB^2+CD^2+EF^2=BC^2+DE^2+AF^2.
N. Sedrakyan
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