An equilateral triangle that has an area of 9 sqrt(3) is inscribed in a circle. What is the area of the circle?
+128406 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
