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five points on a semicircle with radius 1

Source: 4-th Hungary-Israel Binational Mathematical Competition 1993

May 26, 2007
inequalitiestrigonometrysymmetryfunctionvectorinequalities unsolved

Problem Statement

Distinct points A,B,C,D,EA, B , C, D, E are given in this order on a semicircle with radius 11. Prove that AB2+BC2+CD2+DE2+AB⋅BC⋅CD+BC⋅CD⋅DE<4.AB^{2}+BC^{2}+CD^{2}+DE^{2}+AB \cdot BC \cdot CD+BC \cdot CD \cdot DE < 4.
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