MathDB

7

Part of 2002 Iran Team Selection Test

Problems(1)

Spheres

Source: Iran TST 2002

9/27/2006
S1,S2,S3S_{1},S_{2},S_{3} are three spheres in R3\mathbb R^{3} that their centers are not collinear. k≤8k\leq8 is the number of planes that touch three spheres. Ai,Bi,CiA_{i},B_{i},C_{i} is the point that ii-th plane touch the spheres S1,S2,S3S_{1},S_{2},S_{3}. Let OiO_{i} be circumcenter of AiBiCiA_{i}B_{i}C_{i}. Prove that OiO_{i} are collinear.
geometry3D geometryspherecircumcirclepower of a pointradical axisgeometry proposed