Area of Overlapping Circles

Discussion in 'Math' started by Mazaag, Mar 15, 2006.

  1. Mazaag

    Thread Starter Senior Member

    Oct 23, 2004
    255
    0
    Hey guys.

    I need help guys. I know its simple but I have no clue how its done.

    I have two circles, with the same radius, R, and I offset one by a distance X from the origin ( take the center of one of the circles as the origin). I need to calculate the area of the overlapping region. Since the two have the same radii, I assume that it shouldn't be thta complicated, but i'm completely STUCK and can't think ! :S


    Thanks guys,
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    The answer from the following URL is:
    Area of a chord

    Code ( (Unknown Language)):
    1.  
    2. Aoverlap = 2 * (R^2)* arctan[√ (((R/ (0.5*x) )^2) -1)] - x*( √ [R^2 - (x/2)^2] )
    3.  
    4. for x = 0, Aoverlap = pi*R^2 as we expect
    5.  
    6. and for x = 2R, Aoverlap = 0
    7.  
     
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