Problem Solving

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

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

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

Yes the OA is D.

But how did u deduct that the length is 4 since it is an equilateral triangle

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)

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

as others have done,,,

angle =60

thus all sides will b same,,,

thus ans 4!!!

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..