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An equilateral triangle that has an area of 9 sqrt(3)​ is inscribed in a circle. What is the area of the circle?

 Dec 20, 2019
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We can find the radius  of the  circle, R, by using the Law of Cosines

 

We have that

 

(9 sqrt (3))^2 =  2R^2  - 2R^2 ( cos 120°)

 

243  =  2R^2 - 2R^2 * (- 1/2)

 

243 =  2R^2 + R^2

 

243  =  3R^2 

 

Divide both sides by 3

 

81  = R^2   

 

Then the area of the  circle =

 

pi R^2   =

 

pi *81  =

 

81 pi  units^2

 

 

cool cool cool

 Dec 20, 2019

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