   SEARCH HOME Math Central Quandaries & 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? 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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.