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What is the area of the shaded region, if the area of the

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What is the area of the shaded region, if the area of the

by AAPL » Sat Jul 07, 2018 6:37 am

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An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?

$$A.\ 2-3\sqrt{3}$$
$$B.\ 2-\frac{3\sqrt{3}}{\pi}$$
$$C.\ 2-\frac{3\sqrt{3}}{4}$$
$$D.\ 2-\frac{3\sqrt{3}}{2\pi}$$
$$E.\ 2\pi-\frac{3\sqrt{3}}{2\pi}$$

The OA is D.

I don't have clear this PS question. Can anyone give a strategic approach to solve it? Thanks!
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by Jay@ManhattanReview » Mon Jul 09, 2018 12:33 am
AAPL wrote:Image

An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?

$$A.\ 2-3\sqrt{3}$$
$$B.\ 2-\frac{3\sqrt{3}}{\pi}$$
$$C.\ 2-\frac{3\sqrt{3}}{4}$$
$$D.\ 2-\frac{3\sqrt{3}}{2\pi}$$
$$E.\ 2\pi-\frac{3\sqrt{3}}{2\pi}$$

The OA is D.

I don't have clear this PS question. Can anyone give a strategic approach to solve it? Thanks!
Pl. refer to this question: https://www.beatthegmat.com/triangle-in ... 90961.html

Hope this helps.

-Jay
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by Brent@GMATPrepNow » Mon Jul 09, 2018 4:58 am
EXTRA PRACTICE

Here are two more questions involving an equilateral triangle inscribed in a circle:
- https://www.beatthegmat.com/triangle-ins ... 90961.html
- https://www.beatthegmat.com/if-a-smaller ... 89365.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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