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another Sharygin concurrency proposed by A. Zaslavsky (median, circumcircle)

Source: Sharygin 2006 finals 10.4

September 29, 2019
geometryconcurrencyconcurrentmediancircumcircle

Problem Statement

Lines containing the medians of the triangle ABCABC intersect its circumscribed circle for a second time at the points A1,B1,C1A_1, B_1, C_1. The straight lines passing through A,B,CA,B,C parallel to opposite sides intersect it at points A2,B2,C2A_2, B_2, C_2. Prove that lines A1A2,B1B2,C1C2A_1A_2,B_1B_2,C_1C_2 intersect at one point.
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