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Inequality for 5 points in the plane

Source: Japanese MO Finals 2000

February 10, 2011
inequalitiestriangle inequalitygeometry proposedgeometry

Problem Statement

Given five points A,B,C,D,EA,B,C,D,E in a plane, no three of which are collinear, prove the inequality AB+BC+CA+DE≤AD+AE+BD+BE+CD+CEAB+BC+CA+DE\le AD+AE+BD+BE+CD+CE
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