BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Good Circle Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 158
Joined: Mon Nov 02, 2009 5:49 pm
Thanked: 2 times
Followed by:3 members

Good Circle Problem

by tonebeeze » Tue Apr 26, 2011 2:59 pm
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. 4/3
b. 8/3
c. 3
d. 4
e. 6

OA = D
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1255
Joined: Fri Nov 07, 2008 2:08 pm
Location: St. Louis
Thanked: 312 times
Followed by:90 members

by Tani » Tue Apr 26, 2011 3:33 pm
Draw your circle with the center at O. You have a triangle RUO.

Your arc RTU is 4pi/3. The Circumference of the circle is 8pi. Therefore, the arc is 1/6 of hte circumference so the central angel is 1/6 of 360 degrees.

Now draw a third Radius from the center perpendicular to line RU. You will have bisected the central angle and created two 30:60:90 triangles. The hypotenuses of those triangles are the radii (=4), so the sides opposite the 30 degree angles at the center are each 2 units. Therefore, the length of RU is 2*2 = 4 units.
Tani Wolff
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Tue Apr 26, 2011 8:26 pm
tonebeeze 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. 4/3
b. 8/3
c. 3
d. 4
e. 6

OA = D
Refer to the image below,
Image

The measure of the angle subtended by the arc RTU at the center of the circle = (4π/3)/4 = π/3 = 60 degrees

Hence, the triangle ORU is an equilateral one.
Hence, length of the line segment RU = length of the line segment OR = length of the radius = 4

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1