Area between 2 rings

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I would like to know if is possible calculate the area between 2 rings with opposite centers and the same radius, that is:

$$r_1^2<(x-a)^2+(y-b)^2<r_2^2$$ $$r_1^2<(x+a)^2+(y+b)^2<r_2^2$$

I think that depend on the relation between center and radius, but I'm not sure.

I'm working on...

Edit:

This is an example

$$4<(x-1){}^2+(y-2){}^2<8$$

$$4<(x+1){}^2+(y+2){}^2<8$$

Ejemplo

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