space geometry 2
Source: 17-th Iranian Mathematical Olympiad 1999/2000
February 29, 2004
geometry3D geometryspherecircumcircleIran
Problem Statement
Call two circles in three-dimensional space pairwise tangent at a point if they both pass through and lines tangent to each circle at coincide. Three circles not all lying in a plane are pairwise tangent at three distinct points. Prove that there exists a sphere which passes through the three circles.