The radical axis of circles S1=0 and S2=0 is the straight line S1-S2=0. It is the locus of points with equal power with respect to both circles and is always perpendicular to the line joining the centres. For intersecting circles, the radical axis is the common chord. For tangent circles, it is the common tangent at the point of tangency. The radical centre of three circles is the intersection of the pairwise radical axes. The family of circles through the intersection of S1 and S2 is S1+lambdaS2=0. Similarly, S+lambdaL=0 gives circles through the intersection of circle S and line L. Coaxial circles share a common radical axis, and their centres are collinear. Every coaxial system has exactly two limiting point circles (degenerate members with zero radius).
Part of CG-02 — Circles
Radical Axis and Family of Circles
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