Radical axis

The radical axis of two circles is a straight line that represents all the points in the plane where the two circles have equal power with respect to each point. In geometric terms, it is the locus of points from which the lengths of tangents to both circles are equal. This line always exists unless the circles are identical or do not intersect. It helps analyze the relative positions of two circles—whether they intersect, are tangent, or are separate—by serving as a geometric tool to understand their relationships and interplay.