MathDB

Spheres

Source: Iran TST 2002

September 27, 2006

geometry3D geometryspherecircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

S_{1},S_{2},S_{3}

are three spheres in

\mathbb R^{3}

that their centers are not collinear.

k\leq8

is the number of planes that touch three spheres.

A_{i},B_{i},C_{i}

is the point that

i

-th plane touch the spheres

S_{1},S_{2},S_{3}

. Let

O_{i}

be circumcenter of

A_{i}B_{i}C_{i}

. Prove that

O_{i}

are collinear.

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