MathDB
1982 USAMO #5

Source:

August 16, 2011
AMCUSA(J)MOUSAMOgeometry3D geometrysphereconics

Problem Statement

A,BA,B, and CC are three interior points of a sphere SS such that ABAB and ACAC are perpendicular to the diameter of SS through AA, and so that two spheres can be constructed through AA, BB, and CC which are both tangent to SS. Prove that the sum of their radii is equal to the radius of SS.