radical center

The radical center of three circles is the point with the same power with respect to each of the three circles. It is the intersection of the three pairwise radical axes: the radical axis of two circles is the locus of points with the same power with respect to each of them. If the three circles have non-collinear centers, their radical center exists and is unique. The radical center is a fundamental tool in the study of pencils of circles and circle configurations in classical geometry.