JMO 2000 Problem 3

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

Dataset text AoPS wiki problems. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.