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UlisesOrdonez
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UlisesOrdonez
What is the área of an equilateral triangle inscribed in a circle?

1) the area outside the triangle is 3Π
2) radius of the circle is 6

???
When an equilateral triangle is inscribed in a circle, Side of the triangle = √3 * Radius of the circle
\(s = \sqrt{3}r\)

Area of circle \(=pi*r^2\)
Area of triangle \(= \sqrt{3}s^2/4 = 3\sqrt{3}r^2/4\)

Statement 1:
Area outside the triangle \(=pi*r^2 - 3\sqrt{3}r^2/4 = 3*pi\)
You can get r from here and subsequently the area of the triangle

Statement 2:
r is given directly so you can get the area of the triangle.

Answer (D)

Here are some posts on circles and polygons inscribed in them.
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/06 ... d-circles/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/07 ... relations/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/07 ... other-way/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/07 ... n-circles/
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The side of the triangle should be = √2* Radius of the circle, since we have an isosceles triangle with sides r and hypotenuse which is the side of the equilateral triangle

D