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RO-NMO 2010 Problem 92

  • Grade 9

Prove that there is a similarity between a triangle ABCABC and the triangle having as sides the medians of the triangle ABCABC if and only if the squares of the lengths of the sides of triangle ABCABC form an arithmetic sequence.

Marian Teler & Marin Ionescu

Dataset text AI-MO AoPS. Quoted with source.

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