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

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Bunuel
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What is the area of the circle above with center O? [#permalink] New post   20 Aug 2019, 02:28
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What is the area of the circle above with center O?

(1) The area of triangle OAB is 50.

(2) The length of arc ACB is \(15\pi\).


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Re: What is the area of the circle above with center O? [#permalink] New post   20 Aug 2019, 03:42
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Bunuel wrote:

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

(1) The area of OAB is 50.

(2) The length of arc ACB is \(15\pi\).


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#1
The area of OAB is 50
we have an isoscles ∆ so area ; x^2/2 = 50
x=10 ; area is 100pi
sufficient
#2
The length of arc ACB is \(15\pi\).
angle around c ; 270
so r ; 270/360 * 2*pi * r= 15 pi
solve for r = 10 sufficient
IMO D
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Re: What is the area of the circle above with center O? [#permalink] New post   20 Aug 2019, 03:56
Hi Archit3110,

How did you calculate '270' as the angle around C?

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Re: What is the area of the circle above with center O? [#permalink] New post   20 Aug 2019, 03:58
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himanshurajawat wrote:
Hi Archit3110,

How did you calculate '270' as the angle around C?

Posted from my mobile device


see angle BOA= 90* and around center total 360 so angle for arc BCA ; 360-90 ; 270*
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Re: What is the area of the circle above with center O? [#permalink] New post   20 Aug 2019, 05:53
Bunuel wrote:

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

(1) The area of OAB is 50.

(2) The length of arc ACB is \(15\pi\).


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

(1) The area of OAB is 50.
\(r^2/2 = 50\)
r = 10
\(Area = 100\pi\)
SUFFICIENT

(2) The length of arc ACB is \(15\pi\).
\(3/4C = 15\pi\) where C = circumference
\(C = 2\pi r = 20 \pi\)
r = 10
\(Area = 100\pi\)
SUFFICIENT

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Re: What is the area of the circle above with center O? [#permalink] New post   08 Sep 2019, 19:13
VeritasKarishma

What does statement 1 implies? Is it the area of the triangle or the area of the segment?
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Re: What is the area of the circle above with center O? [#permalink] New post   09 Sep 2019, 02:02
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himanshurajawat wrote:
VeritasKarishma

What does statement 1 implies? Is it the area of the triangle or the area of the segment?


It is odd that it is not mentioned whether OAB is the triangle or the sector. An official question would specify clearly. Here, I would just assume that it is the triangle because there is no mention of pi here.
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Re: What is the area of the circle above with center O? [#permalink] New post   19 Sep 2019, 02:33
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VeritasKarishma wrote:
himanshurajawat wrote:
VeritasKarishma

What does statement 1 implies? Is it the area of the triangle or the area of the segment?


It is odd that it is not mentioned whether OAB is the triangle or the sector. An official question would specify clearly. Here, I would just assume that it is the triangle because there is no mention of pi here.


Original question mentions triangle OAB, I copied incorrectly. Edited. Thank you!
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Re: What is the area of the circle above with center O? [#permalink] New post   19 Sep 2019, 02:34
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Bunuel wrote:

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

(1) The area of triangle OAB is 50.

(2) The length of arc ACB is \(15\pi\).


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Attachment:
image794.png


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Re: What is the area of the circle above with center O? [#permalink]
19 Sep 2019, 02:34
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