Radical centre of three circles.

Question

Is radical centre the only point from where equal tangents can be drawn to three circles with non collinear centres. Also in case the radical centre lies inside any of the circle of the three given circles with non collinear centres, will there be no point from where tangents of equal length be drawn to all the three circles?

Answer 1

I think you have a wrong perception about the Radical centre, so let me clarify the definition first. Radical centre is not the point of from where equal tangents can be drawn to three circles with non collinear centres. In fact, it is the point from which power of a point to each of the 3 circles is equal; and since power of point = $ (length of tangent)^2 $ the tangents are equal.

To answer the first part of your question, it can be explained by the property that the radical centre is the point of intersection of the 3 radical axes of the 3 circles; and there exists maximum 1 point of concurrency for 3 distinct lines.

For the second part, well yes but actually no. There will be no such point as tangents are not defined for interior points. BUT but but, there will exist a Radical centre, which will be the point of intersection of the common chords. Also note that this will be possible if all 3 circles are intersecting each other.

I suggest you read further on radical axis, which is the root topic of radical centre.