Geometry Question

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sanaa.rizwan: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Aug 08, 2012 9:00 amFollowed by: 1 member

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 4ÐŸ/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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Source: Beat The GMAT — Problem Solving | Tue Apr 09, 2013 6:34 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

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 4ÐŸ/3, what is the length of the line segment RU

Circumference of the circle = (2ÐŸ)*(4) = 8ÐŸ
Let x be the angle subtended at the center of circle.
Then, 8ÐŸx/360 = 4ÐŸ/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 60Âº.

So, RU = 4

The correct answer is D.

Anju Agarwal
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Deepthi Subbu: Master | Next Rank: 500 Posts; Posts: 298; Joined: Tue Feb 16, 2010 1:09 amFollowed by: 1 member; Thanked: 2 times

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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GMAT/MBA Expert

Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

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,

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.

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