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In the figure, ABC is an equilateral triangle with AB = 6.  Find the area of the circumcircle.

 

 Dec 24, 2019
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We can find the radius of the  circumcircle with the Law of Cosines

 

AB^2  = 2R^2  - 2R^2  cos  (2 * angle BAC)

 

6^2 =  2R^2 - 2R^2 cos (120°)

 

36  =  2R^2  + R^2

 

36 = 3R^2

 

R^2  = 12

 

So....the area of the  circumcircle =   pi * R^2   =  pi * 12  =   12 pi   units^2 

 

 

cool cool cool

 Dec 24, 2019

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