The radical lines of three circles are concurrent in a point known as the radical center
(also called the power center). This theorem was originally demonstrated by Monge
(Dörrie 1965, p. 153). It is a special case of the three
conics theorem (Evelyn et al. 1974, pp. 13 and 15).
The point of concurrence of the three radical lines of three circles is the point
(Kimberling 1998, p. 225).
See also Apollonius' Problem ,
Circle-Circle Intersection ,
Concurrent ,
Monge's
Problem ,
Orthogonal Circles ,
Radical
Circle ,
Radical Line ,
Three
Conics Theorem
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References Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction
to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Coxeter, H. S. M. and
Greitzer, S. L. Geometry
Revisited. Dörrie,
H. 100
Great Problems of Elementary Mathematics: Their History and Solutions. Durell, C. V. Modern
Geometry: The Straight Line and Circle. Evelyn,
C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "The Three-Conics
Theorem." §2.2 in The
Seven Circles Theorem and Other New Theorems. Johnson, R. A. Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Kimberling, C. "Triangle
Centers and Central Triangles." Congr. Numer. 129 , 1-295, 1998. Lachlan,
R. An
Elementary Treatise on Modern Pure Geometry. Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Radical Center
Cite this as:
Weisstein, Eric W. "Radical Center." From
MathWorld https://mathworld.wolfram.com/RadicalCenter.html
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