Position of radical axis for two intersecting circles.

Question

Is it only for two intersecting circles that the radical axis will pass through the interior of the circle or is it also possible in any other case?

Answer 1

Yes. Because The other cases are circles being tangent and non intersecting. For tangent case, radical axis is their line of tangency. For disjoint it is the locus of points at which tangents drawn to both circle have equal length. Now tangents are always outside the circle and two tangent lines can meet only outside. So it is outside both circles. Hence the proof.