Radical axis of 2 circles:
circles intersect, many circles through the two points of intersection, one of them is a straight line, this is the radical axis.
How to find it?
With equations, subtract one equation from the other one – magic, a straight line, and bset of all this works even when the two circles do not intersect.
Saving school math 
Will you explain to me what is this theorem? It is hard to understand the whole concept by just looking/analyzing the figure. 🙂
Radical axis of 2 circles:
circles intersect, many circles through the two points of intersection, one of them is a straight line, this is the radical axis.
How to find it?
With equations, subtract one equation from the other one – magic, a straight line, and bset of all this works even when the two circles do not intersect.