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The three radical axes meet in a single point, the radical center, for the following reason. The radical axis of a pair of circles is defined as the set of points that have equal
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of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the
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of a system of circles, all of the vertices of the diagram are located at radical centers of triples of circles. The
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344:(reprint of 1929 edition by Houghton Mifflin ed.). New York: Dover Publications. pp. 32–34.
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The radical center has several applications in geometry. It has an important role in a solution to
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Advanced
Euclidean Geometry: An elementary treatise on the geometry of the triangle and the circle
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on the radical axis of circles 1 and 2, the powers to each circle are equal:
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242:"Some triangle centers associated with the circles tangent to the excircles"
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100 Great
Problems of Elementary Mathematics: Their History and Solutions
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For 3 circles, the intersection of the radical axes of each pair
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with respect to both circles. For example, for every point
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The
Penguin Dictionary of Curious and Interesting Geometry
44: Radical center (intersection of the radical axes)
50: Radical circle (intersects the given circles
38: Radical axis of each pair of given circles
26:Diagram of the radical center of three circles.
395:An elementary treatise on modern pure geometry
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388:. New York: Dover. pp. 151–154 (§31).
87:) that intersects the three given circles
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147:intersection point of these two lines
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384:Dörrie H (1965). "Monge's Problem".
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397:. London: Macmillan. p. 185.
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483:Radical Axis and Center
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276:Excursions in Geometry
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502:Elementary geometry
340:Johnson RA (1960).
249:Forum Geometricorum
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32: Given circles
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419:Weisstein, Eric W.
393:Lachlan R (1893).
309:Geometry Revisited
279:. Dover. pp.
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321:. pp.
303:Greitzer SL
299:Coxeter HSM
496:Categories
403:B0008CQ720
315:Washington
75:, is the
465:MathWorld
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427:MathWorld
271:Ogilvy CS
217:excircles
172:. Since
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273:(1990).
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