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Source: IMO Shortlist 1993, Indonesia 1

March 25, 2006
geometryratiocircumcircletrigonometryinequalitiesgeometric inequalityIMO Shortlist

Problem Statement

The vertices D,E,FD,E,F of an equilateral triangle lie on the sides BC,CA,ABBC,CA,AB respectively of a triangle ABC.ABC. If a,b,ca,b,c are the respective lengths of these sides, and SS the area of ABC,ABC, prove that DE≥2⋅2⋅Sa2+b2+c2+4⋅3⋅S. DE \geq \frac{2 \cdot \sqrt{2} \cdot S}{\sqrt{a^2 + b^2 + c^2 + 4 \cdot \sqrt{3} \cdot S}}.
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