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What is the area of the circle above with center O?

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by BTGmoderatorDC » Mon Apr 05, 2021 7:19 pm

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A

B

C

D

E

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Untitled.png
What is the area of the circle above with center O?

(1) The length of major arc CA is 27pi
(2) The perimeter of OABC is 72



OA D

Source: Princeton Review
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Source: — Data Sufficiency |
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Re: What is the area of the circle above with center O?

by swerve » Wed Apr 07, 2021 7:20 am
BTGmoderatorDC wrote: ↑
Mon Apr 05, 2021 7:19 pm
 Untitled.png

What is the area of the circle above with center O?

(1) The length of major arc CA is 27pi
(2) The perimeter of OABC is 72



OA D

Source: Princeton Review
The Quadrilateral \(OABC\) is evidently a square as
1. \(OA = OC\)
2. \(\angle{AOC}\) is \(90^{\circ}\)
3. \(\angle{OAB}\) is \(90^{\circ}\) as tangent is perpendicular to radius (as perceived from figure)

So, statement 1 gives the value of \(\pi\cdot\dfrac{(360-90)}{360}\cdot r\), from which \(r\) can be calculated. Sufficient. \(\Large{\color{green}\checkmark}\)

Statement 2 gives the perimeter of the square which is \(4r\) so r can be calculated. Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, D
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