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BCDE parallelogram wanted insides a convex pentagon ABCDE

Source: Ukrainian Geometry Olympiad 2020, IX p5

April 27, 2020
geometryparallelogrampentagonequal anglesequal segments

Problem Statement

Given a convex pentagon ABCDEABCDE, with ∠BAC=∠ABE=∠DEA−90o\angle BAC = \angle ABE = \angle DEA - 90^o, ∠BCA=∠ADE\angle BCA = \angle ADE and also BC=EDBC = ED. Prove that BCDEBCDE is parallelogram.
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