Can you define your terms a bit? What do you mean by “range” and “angle-range?” Also, if you’re taking about angles, angles relative to what in particular? (Maybe relative to the line segment connecting the centers of the two circles? Relative to a tangent of one of the circles at the point of intersection?) Are you looking to solve this only for the case where the two circles have equal radii, or for the more general case where their radii may be unequal?

Also, I’ll assume Euclidian space here. Non-Euclidian isn’t my forte. I guess, though, to say I know nothing about it would be a bit hyperbolic.

I’d suggest using math.