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

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Math Expert
Joined: 02 Sep 2009
Posts: 58100
What is the area of the circle above with center O?  [#permalink]

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20 Aug 2019, 02:28
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Difficulty:

35% (medium)

Question Stats:

72% (01:01) correct 28% (02:02) wrong based on 43 sessions

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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 $$15\pi$$.

Attachment:

image794.png [ 28.08 KiB | Viewed 516 times ]

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Re: What is the area of the circle above with center O?  [#permalink]

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20 Aug 2019, 03:42
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 $$15\pi$$.

Attachment:
image794.png

#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]

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20 Aug 2019, 03:56
Hi Archit3110,

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

Posted from my mobile device
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Re: What is the area of the circle above with center O?  [#permalink]

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20 Aug 2019, 03:58
1
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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What is the area of the circle above with center O?  [#permalink]

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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 $$15\pi$$.

Attachment:
image794.png

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

IMO D
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Re: What is the area of the circle above with center O?  [#permalink]

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08 Sep 2019, 19:13

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]

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09 Sep 2019, 02:02
1
himanshurajawat wrote:

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] 09 Sep 2019, 02:02
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