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R/r >= \sqrt3, sphere contains parallelepiped and it contains another sphere

Source: Polish MO Recond Round 1991 p6

September 9, 2024

geometry3D geometrysphereGeometric Inequalitiesparallelepiped

Problem Statement

The parallelepiped contains a sphere of radius

r

and is contained within a sphere of radius

R

. Prove that

\frac{R}{r} \geq \sqrt{3}