MathDB
sum m_a/h_a <1 + R/r 1989 Kyiv City MO 8.2

Source:

July 17, 2021
geometrygeometric inequality

Problem Statement

Let ha,hb,hch_a,h_b,h_c be the altitudes, and let ma,mb,mcm_a,m_b,m_c be the medians of the acute triangle drawn to the sides a,b,ca, b, c respectively. Let rr and RR be the radii of the inscribed and circumscribed circles. Prove that maha+mbhb+mchc<1+Rr.\frac{m_a}{h_a}+\frac{m_b}{h_b}+\frac{m_c}{h_c} <1+\frac{R}{r}.
Back to ProblemsView on AoPS