In the any [ABCD] tetrahedron we denote with α, β, γ the measures, in radians, of the angles of the three pairs of opposite edges and with r, R the lengths of the rays of the sphere inscribed and respectively circumscribed the tetrahedron. Demonstrate inequality(R3r)3≤sin3α+β+γ(A refinement of inequality R≥3r). tetrahedron3D geometrycircumradiusinradiusinequalitiesgeometry