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AB+BC+CA >= 2CO, triangle in coordinate system

Source: 1985 Swedish Mathematical Competition p5

March 28, 2021
geometryanalytic geometryGeometric Inequalitiesinequalities

Problem Statement

In a rectangular coordinate system, OO is the origin and A(a,0)A(a,0), B(0,b)B(0,b) and C(c,d)C(c,d) the vertices of a triangle. Prove that AB+BC+CA≥2COAB+BC+CA \ge 2CO.
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