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

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
If O is the center of the circle above and the length of arc RSP is tw  [#permalink]

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03 Aug 2018, 02:52
00:00

Difficulty:

15% (low)

Question Stats:

86% (00:46) correct 14% (00:49) wrong based on 58 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

Attachment:

Screen Shot 2015-03-10 at 1.53.19 PM.png [ 16.04 KiB | Viewed 505 times ]

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Manager
Joined: 13 Feb 2018
Posts: 134
Re: If O is the center of the circle above and the length of arc RSP is tw  [#permalink]

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03 Aug 2018, 03:02
Angle POR=x
Outside angle (maybe incorrect interpretation) POR=2x

x+2x=360
x=120

IMO
Ans: C
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 932
WE: Supply Chain Management (Energy and Utilities)
Re: If O is the center of the circle above and the length of arc RSP is tw  [#permalink]

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03 Aug 2018, 06:56
Bunuel wrote:
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
[/spoiler]

$$\widehat{PQR}$$+$$\widehat{RSP}$$=$$Circumference=2\pi*r$$
Or, $$\widehat{PQR}$$+2*$$\widehat{PQR}$$=$$2\pi*r$$
Or, 3*$$\widehat{PQR}$$=$$2\pi*r$$
Or, $$3*2\pi*r(x/360)$$=$$2\pi*r$$
Or, $$x=\frac{360}{3}$$
Or, x=120

Ans. (C)
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PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 03 Nov 2018
Posts: 16
Re: If O is the center of the circle above and the length of arc RSP is tw  [#permalink]

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15 Dec 2018, 11:10
2 + 1 = 3, then 360 degrees has to be divided into three, two of these parts are RSP and one part is PQR. Which makes x = 360/3 = 120.
Re: If O is the center of the circle above and the length of arc RSP is tw &nbs [#permalink] 15 Dec 2018, 11:10
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