Radical axis

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The radical axis of two circles is the locus of points that have the same power with respect to both circles. The radical axis is always a straight line perpendicular to the line through the centers of the circles. If the circles intersect, the radical axis is the line passing through the intersection points, because the power of a point on a circle is zero. Likewise, if the circles are tangent, the radical axis is simply the common tangent.

The radical axis theorem states that the radical axes of three circles (no two of which are concentric) are concurrent (share a common point) or parallel (in this case, they concur at the point of infinity).