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equilaterals AX/XB =BY/YC = CZ/ZA = 2/1 (2022 Novosibirsk Oral Geo Oly 9.6)

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September 3, 2023
geometryEquilateralequilaterals

Problem Statement

Triangle ABCABC is given. On its sides ABAB, BCBC and CACA, respectively, points X,Y,ZX, Y, Z are chosen so that AX:XB=BY:YC=CZ:ZA=2:1.AX : XB =BY : YC = CZ : ZA = 2:1. It turned out that the triangle XYZXYZ is equilateral. Prove that the original triangle ABCABC is also equilateral.
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