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Square ABCD has sides of length 1.  Find the area common to the circles of radius 1 with centers at A and C.

 May 11, 2020
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See the following image

 

 

Using symmetry  the top half of the  common area  can be found as follows :

 

Area of (1/4)circle  with a radius of 1 - Area of right triangle  with  legs of  1  =

 

(1/4) pi (1)^2  - (1/2)(1)^2  =

 

pi/4 -  1/2

 

So.....the  total  common area  =  2 (pi/4 - 1/2)  =  pi/2 - 1 units^2

 

 

cool cool cool

 May 11, 2020

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