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Geometric inequality - ISL 1986

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August 31, 2010
geometry3D geometrytetrahedroninradiusgeometric inequalityIMO Shortlist

Problem Statement

Let ABCDABCD be a tetrahedron having each sum of opposite sides equal to 11. Prove that rA+rB+rC+rD≤33r_A + r_B + r_C + r_D \leq \frac{\sqrt 3}{3} where rA,rB,rC,rDr_A, r_B, r_C, r_D are the inradii of the faces, equality holding only if ABCDABCD is regular.
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