Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to determine the area of intersecting circles?

  1. Oct 27, 2013 #1
    I've been wondering how to calculate the area of intersection of two overlapping circles in terms of their radii. There's two cases I'm interested in:

    The easier case:
    Suppose there are two circles of radius R and r (R > r). The center of the larger circle is at the origin, and the center of the other circle is at (x,y)=(R,0). How can I find the area of the overlap in terms of R and r? I can't think of any clear way to do this by hand.

    The more complicated case:
    Do the same except let the center of the smaller circle lie between (R-r,0) < (x,y) < (R+r,0)

    I've attached a drawing to help show the problem.
    Thanks for any insight. This isn't for school, so there's no rush or anything. Just curious.

    [​IMG]
     
  2. jcsd
  3. Oct 27, 2013 #2
  4. Oct 27, 2013 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    More complicated case is irrelevant. The distance between the centers (and the radii) are all that matter.

    General approach: Get end points of chord which connects the points of intersection of the circles.

    For each circle, calculate the angle made by connecting these end points to the center. Now the problem is reduced to a pair of problems of obtaining for each circle the area of the sector minus the area of the isosceles triangle within the sector.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: How to determine the area of intersecting circles?
  1. Area of a circle (Replies: 2)

Loading...