I have two circles, one of which is completely within the other. They do not touch, but are not necessarily concentric. I am given the sum of their circumferences, and the difference in their areas (ie, the area of the space inside the outer circle and outside the inner circle). I need to find the average distance between the circles or, equivalently, the radii of the circles.
In other words, given $C = C_o + C_i$, and $A = A_o - A_i$, find $R_o$ and $R_i$.
I've gotten as far as expressing $A$ in terms of $C_o$ and $C_i$, but then my long-unused algebra fails me. Any help? Thanks...