Math CentralQuandaries & Queries


Question from Jeff:

I have two circles of different size that overlap one another:
Circle #1 has an area(A) of 731,475, so I can calculate its radius as 482.6.
Circle #2 has an area(A) of 502,517, so I can calculate its radius as 400.

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?


I answered a similar question a couple of years ago. But for this I would recommend formula (14) on the MathWorld page "CircleIntersection":

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.


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