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Geometrical inequality involving the centroid and circumcent

Source: Balkan MO 1996, Problem 1

April 24, 2006
inequalitiesgeometrycircumcircleincenterEulerinequalities proposed

Problem Statement

Let OO be the circumcenter and GG be the centroid of a triangle ABCABC. If RR and rr are the circumcenter and incenter of the triangle, respectively, prove that OG≤R(R−2r). OG \leq \sqrt{ R ( R - 2r ) } . Greece
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