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hexagon, 2 // sides, diagonal divides into quadrilaterals equal perimeters

Source: : Czech-Polish-Slovak Junior Match 2018, individual p2 CPSJ

February 1, 2020
hecagonparalleldiagonalgeometryperimeter

Problem Statement

A convex hexagon ABCDEFABCDEF is given whose sides ABAB and DEDE are parallel. Each of the diagonals AD,BE,CFAD, BE, CF divides this hexagon into two quadrilaterals of equal perimeters. Show that these three diagonals intersect at one point.
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