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Lenth of Line Segment

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by bharathaitha » Thu Oct 23, 2008 4:13 am
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 the line segment RU?

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

pi = 22/7 = 3.14
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by stop@800 » Thu Oct 23, 2008 5:58 am
I think there is some gap with the problem.
Please verify all values.

I am getting ans as 20 * Pi / 3

here is the logic
r = 4
circumference = 8*pi

rtu is 4*pi/3
so remaining (=ru)
is
8*pi - 4*pi/3
= 20 * Pi / 3
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by gmat009 » Thu Oct 23, 2008 6:07 am
stop@800 wrote:I think there is some gap with the problem.
Please verify all values.

I am getting ans as 20 * Pi / 3

here is the logic
r = 4
circumference = 8*pi

rtu is 4*pi/3
so remaining (=ru)
is
8*pi - 4*pi/3
= 20 * Pi / 3
There is no gap in problem.
From circumference and arc you get angle as 60 degree.
So this makes it equilateral triangle
Therefore length of segment is 4
IMO D
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by bharathaitha » Thu Oct 23, 2008 6:32 am
Yes the OA is D.

But how did u deduct that the length is 4 since it is an equilateral triangle
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by rohangupta83 » Thu Oct 23, 2008 7:20 am
imo D

let the centre of the circle be O.
length of the arc = 4*pi/3
radius of the circle = 4
circumference of the circle = 2*pi*r
= 2*pi*4
= 8*pi

Now,

Let angle ROU = x degrees

(4*pi/3)/(8*pi) = x/360

or x = 60 degrees

Therefore, ROU is an equilateral triangle.

Hence, length of side RU is 4 or Choice (D)
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by gmat009 » Thu Oct 23, 2008 7:31 am
bharathaitha wrote:Yes the OA is D.

But how did u deduct that the length is 4 since it is an equilateral triangle
Becoz radius is given as 4
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by raunekk » Fri Oct 24, 2008 1:51 am
as others have done,,,

angle =60

thus all sides will b same,,,

thus ans 4!!!
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Re: Lenth of Line Segment

by sudhir3127 » Fri Oct 24, 2008 4:04 am
bharathaitha wrote: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 the line segment RU?

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

pi = 22/7 = 3.14
D it is ....

Length of the arc = 2*pi* r*theta/360
(4* pi)/3 = 2*pi* 4*theta/360

hence the angle is 60 degrees. = Equvilateral triangle .
hence the legth is 4.

hope its clear..
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