MathDB

1989.8.2

Part of Kyiv City MO 1984-93 - geometry

Problems(1)

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

Source:

7/17/2021
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}.
geometrygeometric inequality