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inradius of tetrahedron, inequality with lengths of nonadjacent edges

Source: Germany MO 2012 - 511345

October 30, 2021
geometryinradius3D geometrytetrahedroninequalitiesgeometric inequality

Problem Statement

Let a,ba,b be the lengths of two nonadjacent edges of a tetrahedron with inradius rr. Prove that r<ab2(a+b).r<\frac{ab}{2(a+b)}.
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