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Problem 5 of Finals

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

September 19, 2019
geometric inequalitygeometry

Problem Statement

Prove that for an arbitrary ΔABC\Delta ABC the following inequality holds: lama+lbmb+lcmc>1\frac{l_a}{m_a}+\frac{l_b}{m_b}+\frac{l_c}{m_c} >1, Where la,lb,lcl_a,l_b,l_c and ma,mb,mcm_a,m_b,m_c are the lengths of the bisectors and medians through AA, BB, and CC.
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