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Medians in right angled triangle

Source: Finnish Mathematics Competition 2010, Final Round, Problem 1

November 15, 2011
geometry unsolvedgeometry

Problem Statement

Let ABCABC be right angled triangle with sides s1,s2,s3s_1,s_2,s_3 medians m1,m2,m3m_1,m_2,m_3. Prove that m12+m22+m32=34(s12+s22+s32)m_1^2+m_2^2+m_3^2=\frac{3}{4}(s_1^2+s_2^2+s_3^2).
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