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Math Help - Area of overlap of two circles.

  1. #1
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    Area of overlap of two circles.

    Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value
    Last edited by mr fantastic; November 28th 2011 at 11:49 AM. Reason: Re-titled.
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    Re: Looking for a solution of this problem

    Quote Originally Posted by leart369 View Post
    Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value
    Here is a way, construct the equilateral triangle inside the shaded area connecting the centers of the circles and one point of intersection. You now know the area of the sector, given by (r^2/2), = pi/3 and you can find the area of the triangle using pythagorean theorem and (base*height)/2

    continue...
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    Re: Looking for a solution of this problem

    Quote Originally Posted by leart369 View Post
    Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value
    If you draw a line segment between the two points of intersection then two circular segments of equal area are formed.
    Go to that webpage. Formula #17 gives the area.
    But there is a problem: Their R is your r.
    There r is your \tfrac{1}{2}r.
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