power line | radical axis

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. Let the circles have radii r_1 and r_2 and their centers be separated by a distance d. 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.

chordal theorem | circle-circle intersection | circle power | coaxal circles | inverse points | inversion | radical center