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IMO ShortList 1988 regular pentagon

Source: IMO ShortList 1988, Problem 17, Israel 2, Problem 47 of ILL

November 3, 2005
geometryconvex polygonpentagonanglesIMO Shortlist

Problem Statement

In the convex pentagon ABCDE, ABCDE, the sides BC,CD,DE BC, CD, DE are equal. Moreover each diagonal of the pentagon is parallel to a side (AC AC is parallel to DE DE, BD BD is parallel to AE AE etc.). Prove that ABCDE ABCDE is a regular pentagon.
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