min and max radius of smallest sphere of 3, tangent to plane, line, each other
Source: VII Soros Olympiad 2000-01 Round 1 , 11.6
July 4, 2021
geometry3D geometryspheregeometric inequality
Problem Statement
Three spheres are tangent to one plane, to a straight line perpendicular to this plane, and in pairs to each other. The radius of the largest sphere is . Within what limits can the radius of the smallest sphere vary?