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please explain gmat prep question

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by jayhawk2001 » Sun Mar 04, 2007 6:14 pm
Arc ABC covers 120 + 120 = 240 degrees

240 / 360 * perimeter = 24
= 2 / 3 * (pi * D) = 24

So, D = 24 * 3 / (2 * pi) which yields 36 / pi which is approx 11
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by yvonne12 » Mon Mar 05, 2007 5:07 pm
I appreciate the time you've taken, could you please tell me how you came to 240.
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by Stacey Koprince » Sun Mar 11, 2007 10:19 pm
It's a bit tough to explain the angles without a diagram. Open up this link to follow along; focus on the 2nd circle on the page:
https://mathworld.wolfram.com/CentralAngle.html

Draw a circle with the inscribed triangle and label your three vertices A, B, and C. Also label arc ABC.

Each angle of the triangle is 60 degrees (since it's equilateral). These angles are called "inscribed angles" because they are on the perimeter of the circle itself. These are the equivalent of the red angle shown in the link I pasted above.

Any inscribed angle is exactly half of its corresponding central angle (which is the blue angle shown in the link I pasted above).

We use the central angle to figure out what portion of a circle we are talking about. Since the arc we want, ABC, covers inscribed angle A (60 degrees) and inscribed angle C (also 60 degrees), the corresponding central angles are double, or 120 and 120. 120 + 120 = 240.
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