Radical Center
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
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. Dublin: Hodges,
Figgis, & Co., p. 43, 1888.
Coxeter, H. S. M. and Greitzer, S. L. Geometry
Revisited. Washington, DC: Math. Assoc. Amer., p. 35, 1967.
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New
York: Dover, 1965.
Durell, C. V. Modern
Geometry: The Straight Line and Circle. London: Macmillan, p. 125, 1928.
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. London: Stacey International,
pp. 11-18, 1974.
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.
Boston, MA: Houghton Mifflin, p. 32, 1929.
Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129,
1-295, 1998.
Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, p. 185,
1893.
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
p. 35, 1991.
Referenced on Wolfram|Alpha:
Radical Center
CITE THIS AS:
Weisstein, Eric W. "Radical Center." From
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