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hexagon with angles, 3 main diagonals and other 6 diagonals, equal, regular?

Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p1

July 30, 2019
hexagonanglesdiagonalsequal segmentsgeometry

Problem Statement

Angles are equal in a hexagon, three main diagonals are equal and the other six diagonals are also equal. Is it true that it has equal sides?