Radical Center

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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. 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.

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Radical Center

Cite this as:

Weisstein, Eric W. "Radical Center." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RadicalCenter.html

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