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equilateral ABC, B_1C_1 = AM, C_1A_1 = BM, A_1B_1 = CM,

Source: III Soros Olympiad 1996-97 R1 10.7 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 29, 2024
geometryEquilateral

Problem Statement

An arbitrary point MM is taken inside a regular triangle ABCABC. Prove, that on sides ABAB, BCBC and CACA one can choose points C1C_1, A1A_1 and B1B_1, respectively, so that B1C1=AMB_1C_1 = AM, C1A1=BMC_1A_1 = BM, A1B1=CMA_1B_1 = CM. Find BABA if AB1=aAB_1= a, AC1=bAC_1 = b, a>ba>b.
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