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medians of inscribed triangle // sides - All-Russian MO 1999 Regional (R4) 8.3

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September 24, 2024
geometryMediansinscribedratio

Problem Statement

On sides BCBC, CACA, ABAB of triangle ABCABC, points A1A_1, B1B_1, C1C_1 are chosen, respectively, so that the medians A1A2A_1A_2, B1B2B_1B_2, C1C2C_1C_2 of the triangle A1B1C1A_1B_1C_1 are respectively parallel to straight lines ABAB, BCBC, CACA. Determine in what ratio points A1A_1, B1B_1, C1C_1 divide the sides of the triangle ABCABC.
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