XK-TST 2012 Problem 3

If $a,b,c$ are the sides of a triangle and $m_a , m_b, m_c$ are the medians prove that $4(m_a^2+m_b^2+m_c^2)=3(a^2+b^2+c^2)$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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