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What is the area of the shaded region?

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by swerve » Fri Apr 20, 2018 8:02 am
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In the above circle, the radius is 6 and chord AB = 6. What is the area of the shaded region?

$$A.\ 2\pi-3\sqrt{3}$$
$$B.\ 4\pi-4\sqrt{3}$$
$$C.\ 4\pi-9\sqrt{3}$$
$$D.\ 6\pi-6\sqrt{3}$$
$$E.\ 6\pi-9\sqrt{3}$$

The OA is E.

Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. Thanks.
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by [email protected] » Fri Apr 20, 2018 4:07 pm
Hi swerve,

We're told that the radius of the circle is 6 and chord AB = 6. We're asked for the area of the shaded region. I'm going to give you a couple of hints/suggestions so that you can retry this question on your own:

1) In most questions that involve a circle, the RADIUS of the circle will almost always play an important role. Here, it's interesting that the radius = 6 AND the chord = 6. If you draw two radii to the two 'ends' of the chord, what shape have you formed?
2) With this triangle, you can determine the measure of the three angles and the area of the triangle.
3) You have the radius of the circle, so you can determine the area of the circle. With the central angle, you can figure out the 'sector area' that is comprised of the triangle and the shaded area.
4) Subtract the area of the triangle from the sector area and you will have the answer.

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