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Convex pentagon is a regular one

Source:

September 15, 2010
geometrycircumcirclepentagonIMO Shortlist

Problem Statement

Prove that a convex pentagon (a five-sided polygon) ABCDEABCDE with equal sides and for which the interior angles satisfy the condition ∠A≥∠B≥∠C≥∠D≥∠E\angle A \geq \angle B \geq \angle C \geq \angle D \geq \angle E is a regular pentagon.
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