1982 USAMO #5
Source:
August 16, 2011
AMCUSA(J)MOUSAMOgeometry3D geometrysphereconics
Problem Statement
, and are three interior points of a sphere such that and are perpendicular to the diameter of through , and so that two spheres can be constructed through , , and which are both tangent to . Prove that the sum of their radii is equal to the radius of .