# Circle-Circle Intersection

1. Jun 25, 2014

### FysixFox

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. Jun 25, 2014

### olivermsun

Solve numerically?

3. Jun 25, 2014

### FysixFox

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.

4. Jun 26, 2014

### olivermsun

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

5. Jun 26, 2014

### FysixFox

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.

6. Jun 26, 2014

### olivermsun

Well, for sure 0 ≤ d ≤ 24, so just try plotting over that interval first and see what happens.

7. Jun 26, 2014

### FysixFox

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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