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equilateral? equal extensions, 6 points concyclic (2021 Kyiv City MO Round2 7.4)

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February 16, 2021
geometryConcyclicEquilateral

Problem Statement

The sides of the triangle ABCABC are extended in both directions and on these extensions 66 equal segments AA1,AA2,BB1,BB2,CC1,CC2AA_1 , AA_2, BB_1,BB_2, CC_1, CC_2 are drawn (fig.). It turned out that all 66 points A1,A2,B1,B2,C1,C2A_1,A_2,B_1,B_2,C_1, C_2 lie on the same circle, is △ABC\vartriangle ABC necessarily equilateral?
(Bogdan Rublev) https://cdn.artofproblemsolving.com/attachments/0/3/a499f6e6d978ce63d2ab40460dc73b62882863.png
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