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The points R, T, and U lie on a circle that has radius 4. If

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The points R, T, and U lie on a circle that has radius 4. If [#permalink] New post 15 Oct 2009, 14:52
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79% (02:12) correct 21% (02:00) wrong based on 68 sessions
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is \frac{4*\pi}{3}, what is the length of line segment RU?

A. 4/3
B. 8/3
C. 3
D. 4
E. 6

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-points-r-t-and-u-lie-on-a-circle-that-has-radius-86376.html
[Reveal] Spoiler: OA
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Re: Geometry Arc? [#permalink] New post 15 Oct 2009, 15:36
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Diameter = 2(Pi)r = 8Pi
Let O be the centre of the circle. Angle of ROU is [(4Pi/3)/8Pi] * 360 = 60
OR = OU =4 (radii) so the triangle ROU is isosceles.
Since angle ROU is 60 this makes the triangle equilateral.
RU = OR = OU = 4
ANS = D
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Re: Geometry Arc? [#permalink] New post 15 Oct 2009, 15:43
2 ( pi) r = x + 4(pi) / 3 .

why will this not work ..
as perimeter of circle should be = length of 2 arc ....
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Re: Geometry Arc? [#permalink] New post 15 Oct 2009, 15:47
pittgreek wrote:
2 ( pi) r = x + 4(pi) / 3 .

why will this not work ..
as perimeter of circle should be = length of 2 arc ....


Not quite sure what X is meant to be in your equation.
4(pi)/3 is a part of the overall diameter which is 2(pi)r = 8(pi).
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Re: Geometry Arc? [#permalink] New post 15 Oct 2009, 16:02
pittgreek wrote:
x= length of RU ...


sorry not absolutely sure where you got the original equation from. The arc (4Pi/3) is defined by a portion of the overall diameter.
Arc + Line Segment will not give you the perimeter of the circle, only of the area bound by the line segment.

Unless I've misunderstood the question what is it asking for is the straight line segment. which will be 4.
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Re: Geometry Arc? [#permalink] New post 17 Oct 2009, 15:15
@ yangsta8
You understood the question right and I think your approach to the solution is also correct. Thanks a lot.
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Re: Geometry Arc? [#permalink] New post 02 Nov 2010, 04:00
Can someone please look at this question? I got 4sqrt{2}
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Re: Geometry Arc? [#permalink] New post 02 Nov 2010, 04:03
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nonameee wrote:
Can someone please look at this question? I got 4sqrt{2}


The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU?
A. 4/3
B. 8/3
C. 3
D. 4
E. 6

The circumference of a circle=2*\pi*r=8*\pi, \frac{RTU}{8*\pi}= \frac{(\frac{4*\pi}{3})}{8\pi}=\frac{1}{6}. --> Angle \angle{RCU}=\frac{360}{6}=60 degrees (C center of the circle).

RCU is isosceles triangle as RC=CU=r and RCU=CRU=CUR=60 degrees. Hence RU=r=4.

Answer: D.

Also discussed here: circle-arc-86376.html?hilit=length%20radius%20segment
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Re: Geometry Arc? [#permalink] New post 02 Nov 2010, 04:13
Oh, yes, thank you, Bunuel. They are referring to the length of arc and not to the measure of a corresponding angle (which is 120 degrees).

Thanks a lot again.
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Re: Geometry Arc? [#permalink] New post 14 Nov 2013, 11:57
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Re: The points R, T, and U lie on a circle that has radius 4. If [#permalink] New post 14 Nov 2013, 12:11
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Re: The points R, T, and U lie on a circle that has radius 4. If   [#permalink] 14 Nov 2013, 12:11
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