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does the hexagon necessarily have a center of symmetry ?

Source: Romania IMO TST 1993 1.3

February 17, 2020
symmetryhexagongeometrydiagonalsequal areas

Problem Statement

Suppose that each of the diagonals AD,BE,CFAD,BE,CF divides the hexagon ABCDEFABCDEF into two parts of the same area and perimeter. Does the hexagon necessarily have a center of symmetry?
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