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

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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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New post 23 Nov 2017, 22:30
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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


[Reveal] Spoiler:
Attachment:
2017-11-23_2026_002.png
2017-11-23_2026_002.png [ 11.63 KiB | Viewed 379 times ]
[Reveal] Spoiler: OA

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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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New post 23 Nov 2017, 23:52
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

Last edited by charan248 on 24 Nov 2017, 00:36, edited 1 time in total.

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

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New post 24 Nov 2017, 00:12
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Answer is C. 120 degrees.

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

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New post 24 Nov 2017, 04:55
Answer:120 degrees

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

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New post 24 Nov 2017, 10:16
Bunuel wrote:
Image
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


[Reveal] Spoiler:
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)

\(\frac{ArcLength}{Circumference}=\frac{Part}{Whole}=\frac{SectorAngleZ}{360}\)

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

\(6Z = 360\) , \(Z = 60\)

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


Answer C

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In the figure above, O is the center of the circle and arc SRT has len   [#permalink] 24 Nov 2017, 10:16
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In the figure above, O is the center of the circle and arc SRT has len

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