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Geometry Question

by sanaa.rizwan » Tue Apr 09, 2013 6:34 pm
QR PS 153

The points R,T and U line on a circle that has a radius of 4. if the length of the arc RTU is 4П/3, what is the length of the line segment RU

a. 4/3
b. 8/3
c. 3
d. 4
e. 6
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by Anju@Gurome » Tue Apr 09, 2013 6:56 pm
sanaa.rizwan wrote:The points R,T and U line on a circle that has a radius of 4. if the length of the arc RTU is 4П/3, what is the length of the line segment RU
Circumference of the circle = (2П)*(4) = 8П
Let x be the angle subtended at the center of circle.
Then, 8Пx/360 = 4П/3
x = 60, now RC and RU are equal so angles CRU and RUC should be equal. Hence, triangle RCU is an equilateral triangle with each angle 60º.

So, RU = 4

The correct answer is D.
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by Deepthi Subbu » Wed Apr 10, 2013 2:34 am
Hi Anju@Gurome,
Since the qn says all the points lie on a circle, the measure of line segment RU is pretty much the same as finding x/360*2*pi*r. i understand that this repeats whats already given, but whats the difference here.?

Also can u illustrate with the help of a diagram pls?
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by Anju@Gurome » Wed Apr 10, 2013 2:47 am
Deepthi Subbu wrote:Hi Anju@Gurome,
Since the qn says all the points lie on a circle, the measure of line segment RU is pretty much the same as finding x/360*2*pi*r. i understand that this repeats whats already given, but whats the difference here.?

Also can u illustrate with the help of a diagram pls?
Refer to the diagram below,
Image

What you've suggested gives us the length of the arc RTU.
But the problem asked for length of the line segment RU.

Hope that helps.
Anju Agarwal
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