MathDB
Geometric Inequality

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September 15, 2010
inequalitiestrigonometrygeometryLaw of SinesquadrilateralIMO Shortlist

Problem Statement

On a semicircle with unit radius four consecutive chords AB,BC,CD,DEAB,BC, CD,DE with lengths a,b,c,da, b, c, d, respectively, are given. Prove that a2+b2+c2+d2+abc+bcd<4.a^2 + b^2 + c^2 + d^2 + abc + bcd < 4.
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