For n+2 spheres in R^n the centers of Apollonius solutions lie on lines concurrent at a single point P_X that is also the center of the generalized inscribed sphere.
Soddy, The Hexlet Nature 138 (1936), 958
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On the Inscribed Sphere and Concurrent Lines through the Centers of Apollonius Spheres in $\mathbb{R}^n$
For n+2 spheres in R^n the centers of Apollonius solutions lie on lines concurrent at a single point P_X that is also the center of the generalized inscribed sphere.