WolframMathWorld gives the following explanation for Radical Circle:
The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at the radical center that is orthogonal to one of the original circles is always orthogonal to all three.)
Is the radical circle always orthogonal to other circles? Or it is orthogonal with all circles only when it is orthogonal with one circle? I am unable to clearly distinguish between these based on the given explanation.