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Circles which share a Radical Line with a given circle are said to be coaxal. The centers of coaxal circles are Collinear. It is possible to combine the two types of coaxal systems illustrated above such that the sets are orthogonal.
See also Circle, Coaxaloid System, Gauss-Bodenmiller Theorem, Radical Line
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 35-36 and 122, 1967.
Dixon, R. Mathographics. New York: Dover, pp. 68-72, 1991.
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 34-37, 199, and 279, 1929.