IR-TST 2002 Problem 7

$S_{1},S_{2},S_{3}$ 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.