You didn't specify whether the circles all had the same radius or not, so I'll assume they don't.
By "3 intersecting circles. Like a Venn Diagram" I assume you mean that circle A partially intersects both circles B and C, circle B partially intersects both circles A and C, and circle C partially intersects both circles A and B so that there are 7 distinct areas bounded by the circles and their intersections (see attachment).
Let's assume that circle A has a radius of r and it's center at (a,b)
Also, circle B has radius s and center (c,d)
And, circle C has radius t and center (e,f)
The formulas for the 3 circles are then:
Circle A: [itex]r^2 = (x-a)^2 + (y-b)^2[/tex]<br />
Circle B: [itex]s^2 = (x-c)^2 + (y-d)^2[/tex]<br />
Circle C: [itex]t^2 = (x-e)^2 + (y-f)^2[/tex]<br />
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Let A be the area of circle A, B be the area of circle B, and C be the area of circle C.<br />
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Call the intersection between circles A and B, area D (the football-like shape)<br />
Similarly, call the intersection between circles B and C, area E and the intersection between circles A and C, area F.<br />
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Lastly, call the intersection of all 3 circles (the diamond-like shaped area in the center), area G.<br />
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If I understand your question correctly, you are looking for A + B + C - D - E - F + 2G<br />
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Note that when you subtract D, for instance, you are already subtracting area G at the same time. So, you again subtract area G when you subtract areas D and F. Therefore, you must add G back in twice.<br />
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At this point, I'll leave the math to you.[/itex][/itex][/itex]
