Given two concentric circles $[C_1,C_2 ]$ with radii $(R_1 < R_2) $ creating an annulus; where should a third circle ($C_3$, radius $R_3$) be located such that the area of intersection between the annulus and $C_3$ is maximum?

When I was trying to solve the problem I assumed WLOG, due to symmetry, that the center of $C_3$ is placed at some point along the x-axis $(d,0)$ and found $d$ to satisfy

$2(R_3^2 + d^2) = R_1^2 + R_2^2$

(If $d$ is not real, then let $d=0$ and all three circles are concentric)

- Is that correct?
- If so, is there a geometrical reason for that criteria?