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area

by ketkoag » Wed May 06, 2009 12:51 am
An equilateral triangle that has an area of 9 3^1/2 is inscribed in a circle. What is the
area of the circle?
A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2
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by sureshbala » Wed May 06, 2009 1:58 am
If an equilateral triangle is inscribed in a circle, 2/3 rd the height of the triangle will be the radius of the circle.


Let "a" be the side of the equilateral triangle.

Given sqrt(3)/4 x a^2 = 9 x sqrt(3)

Hence a^2=36

Thus a = 6.

Now height of the equilateral triangle = sqrt(3)/2 x a = sqrt(3)/2 x 6

Hence radius of the circle = 2/3 x sqrt(3)/2 x 6 = 2 x sqrt(3)

Hence area of the circle = 12 pi
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