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Geometry question - updated :)

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by aj5105 » Fri Jan 02, 2009 8:04 pm
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?
1)4/3
2)8/3
3)3
4)4
5)6
Last edited by aj5105 on Sun Jan 04, 2009 6:52 am, edited 1 time in total.
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Re: ?

by logitech » Fri Jan 02, 2009 8:06 pm
aj5105 wrote:The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is , what is the length of line segment RU?

1)4/3
2)8/3
3)3
4)4
5)6
You forgot to include the lenghth of arc RTU. I was going to back solve all of the options and come up with different RTU's but..I decided not to so :)

For example if RTU is 4pi/3 and the answer is 4 :)
LGTCH
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by rajataga » Sat Jan 03, 2009 2:41 am
if RTU is 4pi/3 and the answer is 4 .....i can understand how this would be calculated, since ORU would become an equilateral traingle...

However, in any other case, how would the length of the chord be calculated...can you please explain this Logitech...

Thanks
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by logitech » Sat Jan 03, 2009 8:12 am
rajataga,

Since this is an only GMAT question we should have a solution for either 60 or 90 degrees solution. Lets wait for poster to update his question.

Thanks,
LGTCH
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by rajataga » Sat Jan 03, 2009 9:29 am
ohhh......

but it can't be 90 degrees, since in that case, the chord would be 4.root3, which isn't there among the options....

another case which could exist would of of 180degrees, in which case the chord could be the diameter, and hence 8, however, again not one of the answer choices.....so the only possible arc could be 4pi/3...

however, is there a formula for calculating the chord length when the angle is say 70 degrees??
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by bsandhyav » Sat Jan 03, 2009 12:34 pm
Ghosh...people here are really something!!! Answers are pouring in even with an incomplete question :wink:

@ Logitech: I'm really glad you removed that target score of 680. You definitely deserve much more !!!!
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by logitech » Sat Jan 03, 2009 4:06 pm
rajataga wrote:ohhh......

but it can't be 90 degrees, since in that case, the chord would be 4.root3, which isn't there among the options....

another case which could exist would of of 180degrees, in which case the chord could be the diameter, and hence 8, however, again not one of the answer choices.....so the only possible arc could be 4pi/3...

however, is there a formula for calculating the chord length when the angle is say 70 degrees??
There is but it is out of GMAT's scope. We should not wake up the sleeping trigonometry giants. :)
LGTCH
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by aj5105 » Sun Jan 04, 2009 6:57 am
guys,I pasted the whole thing - but 4pi/3 was not getting pasted.anyways
it's updated now :)

thanks !
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by vivek.kapoor83 » Sun Jan 04, 2009 9:14 am
4pi/3 = a/360*2pi 4

where a = angle subtended b
y arc.
SO, a = 60
hence, angle is equilateral.
One side =4(given )(radius)
SO, all sides =4
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