diehard_gmat wrote:The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Ï€/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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
