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ASU 094 All Soviet Union MO 1968 octagon with equal angles and integer sides

Source:

June 20, 2019
geometryequal anglesinteger sides

Problem Statement

Given an octagon with the equal angles. The lengths of all the sides are integers. Prove that the opposite sides are equal in pairs.
alternate wording Consider an octagon with equal angles and with rational sides. Prove that it has a center of symmetry.