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parallel wanted starting with a regular heptagon

Source: 2016 Oral Moscow Geometry Olympiad grades 10-11 p2

July 29, 2019
geometryHeptagonparallel

Problem Statement

A regular heptagon A1A2A3A4A5A6A7A_1A_2A_3A_4A_5A_6A_7 is given. Straight A2A3A_2A_3 and A5A6A_5A_6 intersect at point XX, and straight lines A3A5A_3A_5 and A1A6A_1A_6 intersect at point YY. Prove that lines A1A2A_1A_2 and XYXY are parallel.
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