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

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Intern
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The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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New post 23 Aug 2007, 08:16
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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-4-if-168676.html
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Re: PS arc  [#permalink]

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New post 23 Aug 2007, 08:24
minnu wrote:
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is (4π)/3, what is the length of line segment RU?

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

Thanks for help



the triangle becomes equilateral. so RU = 4.
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  [#permalink]

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New post 23 Aug 2007, 08:58
Do a proportion:

[Circumference of Circle] / [Radius of Circle] = [4π/3] / [Length of RU/2]

Let Length of RU = x
Radius = 4
Thus Circumference = 2π(4) = 8π

Thus the Proportion becomes

[8π] / [4] = [4π/3] / [x/2]

Solve for x and you get x = 4/3


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Re: PS arc  [#permalink]

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New post 23 Aug 2007, 08:58
Fistail wrote:
minnu wrote:
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is (4π)/3, what is the length of line segment RU?

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

Thanks for help



the triangle becomes equilateral. so RU = 4.



It is 4!
4p/3 over total circum. which happens to be 8p. We get 1/6 so we know that the arc is 1/6 of the total. 360/6 would be 60 degrees so we have an eq. triangle.
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  [#permalink]

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New post 23 Aug 2007, 19:12
1
Length of arc = angle/ 360 X 2*pi * r = 4 *pi/3

angle = 60 , since r = 4 ( given)

OR= OU = radius = 4

ORU becomes an equilateral triangle, so third side = 4
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Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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New post 08 Apr 2014, 00:58
3
3
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

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-points-r-t-and-u-lie-on-a-circle-that-has-radius-4-if-168676.html
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Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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New post 19 Aug 2018, 11:47
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