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a+h_a > b+h_b > c+h_c if a > b > c, and h_i their altitudes

Source: 1988 Swedish Mathematical Competition p1

March 28, 2021
geometryaltitudesGeometric Inequalities

Problem Statement

Let a>b>ca > b > c be sides of a triangle and ha,hb,hch_a,h_b,h_c be the corresponding altitudes. Prove that a+ha>b+hb>c+hca+h_a > b+h_b > c+h_c.
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