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# If O is the center of the circle above and the length of arc RSP

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Intern
Joined: 29 Mar 2014
Posts: 14
If O is the center of the circle above and the length of arc RSP  [#permalink]

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Updated on: 11 Mar 2015, 04:15
1
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:05) correct 6% (01:16) wrong based on 32 sessions

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If O is the center of the circle above and the length of arc RSP is twice the length of arc PQR, then x equals

(A) 60
(B) 100
(C) 120
(D) 150
(E) 240

Originally posted by pinkcupcake on 10 Mar 2015, 11:20.
Last edited by Bunuel on 11 Mar 2015, 04:15, edited 1 time in total.
Edited the question.
Intern
Joined: 12 Dec 2014
Posts: 2
Re: If O is the center of the circle above and the length of arc RSP  [#permalink]

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10 Mar 2015, 12:23
1
pinkcupcake wrote:
Hi,

Can someone please help me with this question, I am trying to solve it but cannot find the right approach. Thank you.

If O is the center of the circle above and the length of arc RSP is twice the length of arc PQR, then x equals
(A) 60
(B) 100
(C) 120
(D) 150
(E) 240

If x is the angle to be found, the remaining angle at the center is 360-x. Since the arc length ratios are known, x/(360-x) = 1/2, accordingly solve for x to get 120 deg.
Intern
Joined: 02 Nov 2014
Posts: 2
Re: If O is the center of the circle above and the length of arc RSP  [#permalink]

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10 Mar 2015, 12:50
1
Since PSR is twice as long as PQR, you know that there are 3 parts of the circle which have the same length. The whole circle has 360 degrees (you just need to know this fact). As you want to know one arc of the 3 parts that have the same length, you can simply divide 360 by 3 = 120.
Non-Human User
Joined: 09 Sep 2013
Posts: 12082
Re: If O is the center of the circle above and the length of arc RSP  [#permalink]

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06 Aug 2019, 02:13
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Re: If O is the center of the circle above and the length of arc RSP   [#permalink] 06 Aug 2019, 02:13
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