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# In the figure above, O is the center of the circle and arc SRT has len

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
In the figure above, O is the center of the circle and arc SRT has len [#permalink]

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23 Nov 2017, 23:30
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Question Stats:

92% (00:35) correct 8% (00:18) wrong based on 35 sessions

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In the figure above, O is the center of the circle and arc SRT has length 2π. If the circumference of the circle is 12π, what is the value of x + y?

(A) 60
(B) 90
(C) 120
(D) 150
(E) cannot be determined from the information given

Attachment:

2017-11-23_2026_002.png [ 11.63 KiB | Viewed 587 times ]

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In the figure above, O is the center of the circle and arc SRT has len [#permalink]

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Updated on: 24 Nov 2017, 01:36
In the mentioned Question,

Provided that the circumference of the circle is 12π which means Radius is 6 and arc SRT has length 2π which means length is 2X3.14 = 6.28.
Since, two details provided are of no use for the question provided.

If the triangle mentioned is Right angle triangle then answer is 90.

Since no where it is mentioned as Right angle traingle answer must be cannot be determined from the information given which is E

Originally posted by charan248 on 24 Nov 2017, 00:52.
Last edited by charan248 on 24 Nov 2017, 01:36, edited 1 time in total.
Intern
Joined: 29 Aug 2016
Posts: 33
Re: In the figure above, O is the center of the circle and arc SRT has len [#permalink]

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24 Nov 2017, 01:12
1

From the arc length and the circumference we can easily deduce the relationship between the angle subtended by this arc. This comes out to be 60 degrees.

Hence the other two are 120 in total as the sum of interior angles is 180.

Hence C.

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Intern
Joined: 26 Jul 2017
Posts: 5
Re: In the figure above, O is the center of the circle and arc SRT has len [#permalink]

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24 Nov 2017, 05:55

Arc length SRT is 1/6th(2 pi/12 pi) of the total circumference.
So angle POQ is 1/6*360= 60 degrees

That implies x+y= 180-60=120 degrees
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Joined: 22 May 2016
Posts: 1759
In the figure above, O is the center of the circle and arc SRT has len [#permalink]

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24 Nov 2017, 11:16
Bunuel wrote:

In the figure above, O is the center of the circle and arc SRT has length 2π. If the circumference of the circle is 12π, what is the value of x + y?

(A) 60
(B) 90
(C) 120
(D) 150
(E) cannot be determined from the information given

Attachment:
2017-11-23_2026_002.png

Sector ORT, whose arc is SRT, is a fraction of the circle. Let its central angle POQ = ∠Z. From the fraction $$\frac{Sector}{Circle}$$, find ∠Z's measure to find (x + y)

$$\frac{ArcLength}{Circumference}=\frac{Part}{Whole}=\frac{SectorAngleZ}{360}$$

$$\frac{2\pi}{12\pi}=\frac{1}{6}=\frac{Z}{360}$$

$$6Z = 360$$ , $$Z = 60$$

$$∆ OPQ: (x + y + Z) = 180$$
$$x + y + 60 = 180$$
$$x + y = 120$$

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In the figure above, O is the center of the circle and arc SRT has len   [#permalink] 24 Nov 2017, 11:16
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