Circles of Power cannot effectively "overlap" in such a way that you count as being within two circles at once. Instead, a Circle around another Circle is (for purposes of using the Circle) more of a "donut" shape than anything.
Thus, nothing happens to someone within the inner Circle of Power if someone begins a ritual in the outer Circle of Power (other than ritual effects which would normally target everyone nearby, for example, a Backlash which affects everyone "in line of sight" of the Circle which hosts the Backlashing ritual).
-Bryan Gregory
ARC