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

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Intern
Joined: 19 Aug 2007
Posts: 18
The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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23 Aug 2007, 08:16
6
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:08) correct 26% (01:32) wrong based on 185 sessions

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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
Director
Joined: 03 May 2007
Posts: 763
Schools: University of Chicago, Wharton School

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23 Aug 2007, 08:24
1
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.
Intern
Joined: 14 Feb 2007
Posts: 24

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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
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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Manager
Joined: 22 May 2007
Posts: 110

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23 Aug 2007, 08:58
1
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.
Manager
Joined: 18 Jun 2007
Posts: 83

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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
Math Expert
Joined: 02 Sep 2009
Posts: 55732
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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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 $$RU=r=4$$.

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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Joined: 09 Sep 2013
Posts: 11398
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

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19 Aug 2018, 11:47
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Re: The points R, T, and U lie on a circle that has radius 4. If   [#permalink] 19 Aug 2018, 11:47
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