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 theorm, 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 circles intersect 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

their radical line has equation

(Kimberling 1998, p. 224).

The radical line is located at distances

along the line of centers from and , respectively, where

The radical line of any two polar circles is the altitude from the third vertex.