Difference between revisions of "Radical axis"
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Revision as of 22:26, 30 April 2009
The radical axis of two circles 
is defined as the locus of the points 
such that the power of with respect to are equal. If 
are the center and radius of 
, then we say that for any point on the radical axis, ![\[PO_1^2 - r_1^2 = PO_2^2 - r_2^2\]](http://latex.artofproblemsolving.com/8/7/b/87be0c12637822df7a8654ea24005bf39ae11175.png)
The radical axis is a line. If the two circles intersect at two common points, their radical axis is the line through these two points (because the power of each of the common points is 
); if they intersect at one point, their radical axis is the common internal tangent.
The three pairwise radical axes of three circles concur at a point, called the radical center.
