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find out chord length

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by jeevan.Gk » Sat Jan 31, 2009 2:51 am
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

Pls explain if any properties are used
Last edited by jeevan.Gk on Sat Jan 31, 2009 10:47 pm, edited 1 time in total.
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by ontopofit » Sat Jan 31, 2009 3:17 am
plz specify the length of arc RTU
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by jeevan.Gk » Sat Jan 31, 2009 10:48 pm
Sorry ! . Edited
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by krisraam » Sat Jan 31, 2009 11:04 pm
Answer is D

The angle made by the chord at the center is 60. The angle made by the sides of the triangle to the diameter is 60.

See the image for more detail

Thanks
Raama


[/img][/url]
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by DeepakR » Sun Feb 01, 2009 3:12 am
Let O be the Center of the circle. Length of arc RTU = [(angle)/360] * 2piR
equate it with the given length 4pi/3 and find the angle=60. Since OR=OU=4 radius and angle between them =60 (we found above) the triangle ORU must be an equilateral triangle > hence the length of the side RU must also be 4.

- Deepak
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