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Area of intersection between two circles

  1. Jul 28, 2013 #1
    Hi,

    I would very much like someone to help me solve the area of intersection between to intersecting circles (one with the radius r, and one with the radius 1). Tangents at the intersecting point form a 120 degree outer angle.

    1. The problem statement, all variables and given/known data, 2 Relevent equations

    Here is a sketch of the problem: http://i42.tinypic.com/m9254i.jpg
    I want to calculate the area of the intersection between the two circles.

    3. The attempt at a solution

    I've tried to calculate the distance between the centres of the two circles and thought I could use that to somehow calculate the area of the intersection but I haven't managed to find any solution to the problem.


    Thank you so much for your time and help.

    Sincerely,
    Sarah
     
  2. jcsd
  3. Jul 29, 2013 #2

    haruspex

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    Hi Sarah,
    If you draw a line joining the two points of intersection, you will cut the area into two segments. Can you see how to calculate the area of one of these segments (as the difference of two simpler areas)?
     
  4. Jul 29, 2013 #3

    lurflurf

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    Concentrate on the sectors of intersection (there is no intersection in the rest of the circles).

    Area intersection=Area sector 1+Area sector 2-Area union of sectors
    The union of sectors is the kite (quadrilateral with two pairs of adjacent equal sides) the two sectors form
    The idea is the overlap is the double conted area so we can add the two areas and subtract the single counted part to find it.

    usefull formula
    area sector=(angle/angle full circle)pi r^2
    area kite=rR sin (angle)
    r R radii two circles
    angle angle between unequal sides
    length of chord 2r sin(angle/2)
     
  5. Jul 29, 2013 #4

    verty

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    The first thing is to find angles MCO and MOC in terms of r.
     
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