Circle

[bia]

My answer is : 4sqrt(3). Anyone has the same answer as I ?

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

[luvaduva]

I get B) 4.

Basically, you use the fact that the arc length is 1/6 the circumference to determine that the angle of the arc is 60 and use 30-60-90 triangle properties.

A picture is worth a thousand words so...

[bia]

Ok, I'm wrong in calculating arc RTU. Thanks

[netigen]

no need to complicate such a simple problem.

when we find out that the arc angle is 60 we know that the triangle is an equilateral triangle. This means all sides should be equal hence RU=4

[moneyman]

Hi Netigen..how did u conclude that if the triangle is an equilateral triangle ? It can be a 30-60-90 as well right ? Or am I missing something ?

[Stuart@KaplanGMAT]

Hi Netigen..how did u conclude that if the triangle is an equilateral triangle ? It can be a 30-60-90 as well right ? Or am I missing something ?

Every triangle formed with 2 radii is going to be isosceles, since radius = radius. The two angles NOT at the centre of the circle will always be equal. If we let "c" be the angle at the centre and x be the two angles on the circumference, we know that:

180 = c + 2x

In this question, c = 60, so

180 = 60 + 2x
120 = 2x
60 = x

So, our triangle must be 60/60/60, i.e. equliateral.