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Hart's Theorem

Any one of the eight Apollonius Circles of three given Circles is Tangent to a Circle $C$, 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


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.

© 1996-9 Eric W. Weisstein