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by aniruddhkashyap » Thu Apr 22, 2010 8:58 pm
The question is as follows

Q8: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3, what is the length of line segment RU?

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

The book gives the answer as D but according to me it should be A
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by Rahul@gurome » Thu Apr 22, 2010 10:01 pm
Let the centre of the circle be 0.
Let the arc RTU subtend angle x at O.
So length of arc RTU is (x/360) * 2*pi*radius = (x/360) * 2 * pi * 4 = (4/3)*pi { given in the question}.
So x = 60
Now triangle ROU is isosceles because RO and OU are radius and angle ROU is 60.
So angle OUR = angle ORU =(180 -60)/2 = 60.
So triangle ROU is an equilateral triangle and hence all sides are equal.
Or OR = OU = RU = 4

The correct answer is D..
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by akhpad » Fri Apr 23, 2010 7:33 am
Agree that RU = 4

First find angle subtended by arc at center = 60. Adjacent sides are equal.

So, it should be equilateral triangle.
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by poohv005 » Fri Apr 23, 2010 11:26 am
To find the length of RU we need to find the angle of the arc RTU,
X = (360*4pi/3)/2pi(4) = 60

This implies that all the angle of triangle formed in circle is 60

therefore all the sides are equal and so RU is 4
answer is D.
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by Stuart@KaplanGMAT » Fri Apr 23, 2010 4:56 pm
aniruddhkashyap wrote:The question is as follows

Q8: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3, what is the length of line segment RU?

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

the algebra in the other answers is just fine, so I just want to review the general formula for this type of question, the circle sector formula.

For a sector of a circle with degree measure x and that's formed by minor arc AB, we have:

x/360 = AB/circumference = area of sector/area of circle

Questions involving circle sectors almost always come down to some application of that formula.
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by aniruddhkashyap » Wed May 05, 2010 9:02 pm
Need help with the following DS questions

Q7:
Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

Q36:
If n is an integer and 100 < n <200, what is the value of n?
(1) 36n is an odd integer.
(2) 45n is an even integer.
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