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| Math Central | Quandaries & Queries |
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Question from Jeff: I have two circles of different size that overlap one another: If I know that the area where they overlap is 179,271, how can I calculate the distance between the midpoints of these two circles? |
Jeff,
I answered a similar question a couple of years ago. But for this I would recommend formula (14) on the MathWorld page "CircleIntersection":
http://mathworld.wolfram.com/Circle-CircleIntersection.html
Plug the numbers r = 482.53 (NOT 482.6) and R = 400 into equation (14). I would then keep guessing different values of d until getting an area as close as desired to 179,271. The alternative would be to use a computer program that numerically solves equations involving inverse cosines and square roots.
Chris
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