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

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What is the area of the circle above with center O. [#permalink] New post 01 May 2013, 04:32
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

85% (01:31) correct 14% (00:44) wrong based on 28 sessions
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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

[Reveal] Spoiler:
I choose A, but the OA is D. Please help me understand the solution.
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 May 2013, 04:36, edited 1 time in total.
Edited the question.
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Re: What is the area of the circle above with center O. [#permalink] New post 01 May 2013, 04:40
The Quadrilateral OABC is evidently a square as
1. OA = OC
2. /_AOC is 90deg.
3. /_OAB is 90deg. as tangent is perpendicular to radius (as percieved from figure)

So statement A gives the value of pi*(360-90)/360*r, from which r can be calculated

Statement B gives the perimieter of the square which is 4r so r can be calculated

Both are independently sufficient
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Re: What is the area of the circle above with center O. [#permalink] New post 01 May 2013, 06:21
aceacharya wrote:
The Quadrilateral OABC is evidently a square as
1. OA = OC
2. /_AOC is 90deg.
3. /_OAB is 90deg. as tangent is perpendicular to radius (as percieved from figure)

So statement A gives the value of pi*(360-90)/360*r, from which r can be calculated

Statement B gives the perimieter of the square which is 4r so r can be calculated

Both are independently sufficient

You have assumed that quadrilateral is a square. My question and doubt is precisely that, to which level we can assume things from the figure? It is not mentioned in question that AB and CB is tangent to the circle.
Re: What is the area of the circle above with center O.   [#permalink] 01 May 2013, 06:21
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