Radical Line
The Locus of points of equal Power with respect to two nonconcentricCircles which is Perpendicular to the line of centers (the Chordal Theorem; Dörrie 1965).Let the circles have Radii 
and 
and their centers be separated by a distance 
. If theCircles intersect in two points, then the radical line is the line passing through the points ofintersection. If not, then draw any two Circles which cut each original Circle twice. Draw linesthrough each pair of points of intersection of each Circle. The line connecting their two points of intersection isthen the radical line.
The radical line is located at distances
 |  |  | (1) |
 | |  | (2) |
along the line of centers from
and 
, respectively, where | (3) |
The radical line of any two Polar Circles is the Altitude from the third vertex.
See also Chordal Theorem, Coaxal Circles, Inverse Points, Inversion, Power (Circle),Radical Center
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 31-34, 1967. Dixon, R. Mathographics. New York: Dover, p. 68, 1991. Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 153, 1965. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 28-34 and 176-177, 1929.
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