I do believe that logically, you're speaking about the Distance formula.
Distance between two points = squareroot( (x2-x1)(x2-x1) + (y2-y1)(y2-y1) + (z2-z1)*(z2-z1)). If you set a variable equal to that formula, where x1 is the center and x2 is the position your limiting from. You could then rotate x2 based on x1's coordinate system. I hope I am understanding you question.
Isn't what you mean simply the vector length of the radius of a circle? I have no idea what all this polar stuff is everyone seems to be mentioning. But if angle isn't part of the equasion, just ignore it right? Leaving behind one thing, a 2 dimensional line with a length. So why make it more complex than that, since the angle can't change the length