# How to check if circles intersect each other?

I'm trying to do trilateration where I know the coordinates of three known points and the estimates of the radii - not guaranteed to be really precise. My question is, how can I check if the circles actually intersect each other? Does the checking step mentioned in this tutorial make sense, considering the estimate values?

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Two circles intersect each other if the distance of the middle points is smaller than the sum of their radii. Does this help? –  Listing Jun 2 '11 at 12:30
Yes, I know. The problem is I don't know the exact value of the radii because I estimate them based on other parameters (e.g. Bluetooth signal strength values). So, does it somehow still make sense to check if they actually intersect, or just go with the rest of the calculation? –  printemps Jun 2 '11 at 12:44
Sure it does but of course you will get an error in the end that depends on the error in the calculation of the radii. –  Listing Jun 2 '11 at 12:47
Thanks! I'll get back to you if there's any further issues. –  printemps Jun 2 '11 at 12:55

## 1 Answer

If by the checking step you mean the first three lines in the tutorial, it does make sense. It sounds like your center points are known well, even if the distances are not. For two circles, each with a range of radii, you can do two checks-one with the minimum radii and one with the maximum. For the most part, you will then know if they intersect none, some, or all of the time the radii are in that range. There are pathological cases where the intersection will disappear in the middle. One example would be center $(0,0)$, distance $(\frac{5}{8},\frac{7}{8})$ and center $(1,0)$ distance $(\frac{1}{2},\frac{7}{4})$. If the error in you distance estimates is small, this is unlikely.

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Thanks! That will do the trick. –  printemps Jun 3 '11 at 7:42