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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: 49911
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, 03:52
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Difficulty:

15% (low)

Question Stats:

85% (01:00) correct 15% (01:38) wrong based on 41 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

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Joined: 13 Feb 2018
Posts: 135
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, 04:02
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: 890
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, 07:56
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

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Re: If O is the center of the circle above and the length of arc RSP is tw &nbs [#permalink] 03 Aug 2018, 07:56
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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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