Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$.
Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively.
For the given values $n(A)=a$, $n(B)=b$, and $n(A \cap B)=c$, find the relationship of their centers in terms of $a$, $b$, and $c$.
The objective is to draw both inner circles.