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Circle-Circle Intersection

  1. Jun 25, 2014 #1

    FysixFox

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    Okay, so I've found out about how circle-circle intersection works ( http://mathworld.wolfram.com/Circle-CircleIntersection.html ). I'm working with the following knowledge:

    1. The area of the overlap is 100
    2. The two circles have the same radius, 12
    3. d is unknown

    How would I solve for d in the following equation?

    A = 2r2arccos(d/2r) - 0.5sqrt(4r2d2 - d4)

    or, with the values put in:

    100 = 288arccos(d/24) - 0.5sqrt(576d2 - d4)
     
  2. jcsd
  3. Jun 25, 2014 #2

    olivermsun

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    Solve numerically?
     
  4. Jun 25, 2014 #3

    FysixFox

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    Numerically. Or at all. I don't know what to do when there's all this arccos and square root stuff everywhere aand I can't find out how to isolate d.
     
  5. Jun 26, 2014 #4

    olivermsun

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    One way is to arrange your equation in any convenient way you like, and graph the left and right sides as functions of d.
     
  6. Jun 26, 2014 #5

    FysixFox

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    The problem is, there's only one possible answer for d. How would I even know if I got close? I mean, I know it's less than 24 and proooobably more than 12, but... that's just from thinking about the circles on a graph.
     
  7. Jun 26, 2014 #6

    olivermsun

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    Well, for sure 0 ≤ d ≤ 24, so just try plotting over that interval first and see what happens.
     
  8. Jun 26, 2014 #7

    FysixFox

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    Hm, let's use a graphing software to save time... Aha! It seems that the equation works when d is slightly less than 15.95... thanks! :)
     
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