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I have equasion to calculate area of two circles with common part.

Equasion common part

But actually I just need to know if two cirlces have common part or no. Is there simpler equasion for that task? Can't find anything for hours...

For example: Two circles

instead
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3 Answers3

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Calculating the distance between their centres, if it if less then the sum of the radii then they have a common part.

James Screech
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  • You're right but that would work IF two circles have ther center on the same height. I'll edit my question. – instead Apr 27 '16 at 13:01
  • The distance between the centres can be calculated by Pythagoras if they are at different heights. Square the centre differences in x, add this to the square of the centre differences in y. Then take the square root of the answer. If this is greater than the sum of the two radii then the circles do not overlap. – James Screech Apr 27 '16 at 13:16
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If one circle is centered at $(x_1,y_1)$ with radius $r_1$ and the other circle is centered at $(x_2,y_x)$ with radius $r_2$, then they have a common part if and only if

$$(x_1-x_2)^2+(y_1-y_2)^2\le(r_1+r_2)^2$$

Note, in the case of equality, the common part is a single point, where the two circles are tangent.

Barry Cipra
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  • Great! That's what I was looking for. Thank You. Unfortunately I can't upvote Your answer yet (15 rep). – instead Apr 27 '16 at 13:21
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If $$d<r_1+r_2$$ where $r_1$ and $r_2$ are the radii of the two circles, and $d$ is the distance between their centers. If this inequality is true, then they contain an overlapping section.

Drew Christensen
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