I took a similar approach to Chetan4u, but worked with a square inside the circle instead of a triangle.

If you inscribe a square inside a circle, then there will be 4 small regions inside the circle but outside the square. The question is asking us to find the area of two of these regions. Pictures are so much easier:

Attachment:

Square in circle.png [ 4.56 KiB | Viewed 2073 times ]
Now, the area of the circle is \(\pi r^2 = 4\pi\)

The length of one side of the square is \(\sqrt{2^2+2^2} = \sqrt{8}\)

So the area of the square is \((\sqrt{8})^2 = 8\)

And the area of the shaded region is half the area outside the square

\(\frac{1}{2}(4\pi-8) = 2\pi-4\)

Answer: C

*For some reason the math editor is adding a vertical line at the end of each expression... it is not part of the expression and should be ignored.

_________________

Dave de Koos

GMAT aficionado