FI-MO 2010 Problem 1

Let $ABC$ be right angled triangle with sides $s_1,s_2,s_3$ medians $m_1,m_2,m_3$ . Prove that $m_1^2+m_2^2+m_3^2=\frac{3}{4}(s_1^2+s_2^2+s_3^2)$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.