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IZhO 2024 Problem 6

    The medians of a triangle ABCABC concur at point GG. Among the six angles GAB,GAC,GBA,GBC,GCA,GCBGAB, GAC, GBA, GBC, GCA, GCB there are at least three angles each of which is at least α\alpha. Determine the largest α\alpha for which this is possible.

    Official text International Zhautykov Olympiad 2024 official paper, page 1. Quoted with source.

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