diehard_gmat wrote:The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4π/3, what is the length of line segment RU?
A. 34
B. 38
C. 3
D. 4
E. 6
Circles display the following proportionality:
(Central Angle)/360 = (intercepted arc length)/circumference
Here's a drawing of the problem above:
(Central angle ∠ROU)/360 = (intercepted arc RTU)/circumference.
Circumference = 2�r = 8�.
Arc RTU/Circumference = (4�/3)/8� = 1/6.
Thus, central angle ∠ROU = 1/6 * 360 = 60.
Since OR and OU are radii, they are equal. Thus, the angles opposite OR and OU in triangle ORU must also be equal.
Thus, ∠ORU = ∠OUR = 60.
Thus, triangle ORU is equilateral, so RU = 4.
The correct answer is
D.
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