What is the area of the circle above with center O?
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(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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The Quadrilateral \(OABC\) is evidently a square asBTGmoderatorDC wrote: ↑Mon Apr 05, 2021 7:19 pmUntitled.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
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