Geometry question - updated :)

[aj5105]

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

[logitech]

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

[rajataga]

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

[logitech]

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,

[rajataga]

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??

[bsandhyav]

Ghosh...people here are really something!!! Answers are pouring in even with an incomplete question

@ Logitech: I'm really glad you removed that target score of 680. You definitely deserve much more !!!!

[logitech]

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.

[aj5105]

guys,I pasted the whole thing - but 4pi/3 was not getting pasted.anyways
it's updated now

thanks !

[vivek.kapoor83]

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