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Inequality in a tetrahedron

Source: Vietnam TST 1990, Problem 5

July 29, 2008
inequalitiesgeometry3D geometrytetrahedrontrigonometrygeometry unsolved

Problem Statement

Given a tetrahedron such that product of the opposite edges is 1 1. Let the angle between the opposite edges be α \alpha, β \beta, γ \gamma, and circumradii of four faces be R1 R_1, R2 R_2, R3 R_3, R4 R_4. Prove that \sin^2\alpha \plus{} \sin^2\beta \plus{} \sin^2\gamma\ge\frac {1}{\sqrt {R_1R_2R_3R_4}}
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