# Math Help - overlapping circles

1. ## overlapping circles

Given the centers of the circles(say points a,b,c,d,e) and a fixed radius 'r'. The circles may be overlap each other. How to find the area of a given circle that is not overlapping with any other circles.

if there are only two circles we can easily find out the common area and subtract it from the circles area. But as there are more than two circles we cant directly subtract the common areas by considering two points at a time...

help me plzz....

2. Originally Posted by rockey191
Given the centers of the circles(say points a,b,c,d,e) and a fixed radius 'r'. The circles may be overlap each other. How to find the area of a given circle that is not overlapping with any other circles.

if there are only two circles we can easily find out the common area and subtract it from the circles area. But as there are more than two circles we cant directly subtract the common areas by considering two points at a time...

help me plzz....
Confused wording.

Try: given a set of circles (all with the same radius r?) find the total area within the circles that does not belong to a region of overlap between two or more of the circles. Or find the total area within a given circle that does not belong to a region of overlap with any of the other circles.

CB

3. Originally Posted by rockey191
Given the centers of the circles(say points a,b,c,d,e) and a fixed radius 'r'. The circles may be overlap each other. How to find the area of a given circle that is not overlapping with any other circles.

if there are only two circles we can easily find out the common area and subtract it from the circles area. But as there are more than two circles we cant directly subtract the common areas by considering two points at a time...

help me plzz....
[Delaunay triangulation.]
Select your primary circle.
You can quickly EXCLUDE all other circles that are more that 2r away from the center of the Primary.
Use Delaunay calculations to minimize the numer of other circles in the over lap.

Then (in a clockwise or counterclockwise direction) determine the intersection points with the Primary, or with a previous circle.

You will end with a series of connected convex arcs (and perhaps some concave arcs) that are not in any overlap.
To the area of that resulting polygon, you need to add the concave segments, and subtract the convex segments.

There are other procedures you can use, but the delaunay method determines the nearest neighboring circles. (With this, the radii are not required to be constant).