The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two
nonconcentric circles. By the chordal
theorem, it is perpendicular to the line of
centers (Dörrie 1965).
Let the circles have radii and and their centers be separated by a distance . If the circlesintersect
in two points, then the radical line is the line passing through the points of intersection.
If not, then draw any two circles which cut each original
circle twice. Draw lines through each pair of points of
intersection of each circle. The line connecting their
two points of intersection is then the radical line.
Given two circles with trilinear equations
(1)
their radical line has equation
(2)
(Kimberling 1998, p. 224).
The radical line is located at distances
(3)
(4)
along the line of centers from and , respectively, where