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Any one of the eight Apollonius Circles of three given Circles
is Tangent to a Circle 
, as are the other three Apollonius Circles
having (1) like contact with two of the given Circles and
(2) unlike contact with the third.
See also Apollonius Circles
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 127-128, 1929.