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

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by BTGmoderatorDC » Mon Sep 28, 2020 5:48 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 » Tue Sep 29, 2020 1:02 pm
BTGmoderatorDC wrote: ↑
Mon Sep 28, 2020 5:48 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)

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

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

Both are independently sufficient.

Therefore, D
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