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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.

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    When you say 'relationship', do you mean distance? Also, apart from giving bounds for $a$, $b$ and $c$, $S$ doesn't really do anything, does it?2012-07-12
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    You've tried making a drawing?2012-07-12
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    @J.M.: I haven't drawn it yet because there might be many solutions.2012-07-12
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    If you're trying to draw an area-proportional Venn diagram, you could have $a=b=\frac12$ but $c=0$, in which case there is no solution.2013-01-22
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    *there might be many solutions*... Are you sure? For any given values of $a$ and $b$, any $0\lt c\lt\min(a,b)$ uniquely determines the distance between their centers.2013-01-26
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    It may be best to ignore the outer circle, and focus on getting the three areas inside one or both circles proportional to their assigned probabilities. Because if the required area for $c$ is small in comparison to $a$ and $b$, the solution ignoring the outer circle might look like two large circles overlapping only a little bit, and if that is put inside a "universe" circle it severely limits how small the complement of the union of A,B can be.2013-05-06

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