Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49968

The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
11 Mar 2014, 23:58
Question Stats:
70% (02:18) correct 30% (02:33) wrong based on 933 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionThe points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is \(\frac{4*\pi}{3}\), what is the length of line segment RU? (A) 4/3 (B) 8/3 (C) 3 (D) 4 (E) 6 Problem Solving Question: 153 Category: Geometry Circles; Triangles; Circumference Page: 82 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 49968

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
11 Mar 2014, 23:59




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
Updated on: 07 May 2014, 02:08
Answer = (D) 4 Perimeter of Circle \(= 8 \pi\) Perimeter of arc \(= 4 \frac{\pi}{3}\) So, \(8 \pi * \frac{1}{6} = 4 \frac{\pi}{3}\) means Perimeter of arc is \(\frac{1}{6}\) th the Perimeter of Circle So Angle ROU\(= \frac{360}{6} = 60\) Deg Triangle ROU was already an isosceles triangle (as inscribed in circle) with equal sides = 4 Now as its a equilateral triangle, RU = 4
Attachments
rt.jpg [ 14.41 KiB  Viewed 10401 times ]
_________________
Kindly press "+1 Kudos" to appreciate
Originally posted by PareshGmat on 12 Mar 2014, 20:28.
Last edited by PareshGmat on 07 May 2014, 02:08, edited 1 time in total.




Intern
Joined: 10 Apr 2008
Posts: 25
Location: India
WE: Consulting (Computer Software)

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
25 Dec 2014, 02:45
I think the important point here is to understand the transition from isosceles triangle to equilateral. If you can quickly see that despite being isosceles, it is also equilateral triangle, you will be able to answer the Q. I missed this point and ended up marking wrong answer..



Manager
Joined: 26 Feb 2015
Posts: 115

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
09 Apr 2015, 06:58
So if the circumference of the circle is 8 (since radius 4). So 360 degrees is 8pi. (4pi/3)/8pi is 1/6. So RTU has at least one angle with 60 degrees, the other angles could be 30 + 90 or 60 + 60, or am I misintepreting the question?



Math Expert
Joined: 02 Sep 2009
Posts: 49968

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
09 Apr 2015, 07:08



Wharton Thread Master
Joined: 30 May 2015
Posts: 39

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
11 Feb 2017, 14:01
Let consider O as the centre of circle and r as radius 2πr * ((∠ROU)/360) = 4π/3 After solving it ∠ROU = 60 now OR = OU (Radius of the circle) which means ∠ORU = ∠OUR = 60 (Opposite angles of two opposite sides will be equal and some of three angles of triangle is 180) as all three angles are 60 degree, which means it is equilateral triangle. So Answer => OR = OU = RU = 4



Manager
Joined: 21 Jun 2017
Posts: 83

The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
11 Oct 2017, 12:39
Given radius is 4, you immediately know that triangle ROU is an Isosceles. But, since we are not given the degrees, we do not know at first if the triangle is an equilateral.
Circumference of a circle = 2pi r = 8pi arc = x/360(circumference)
4pi/3/8pi = x/360 480/8pi = 60 = x
So, with 60 degrees as our angle in triangle ROU, and with two sides equal, we can deduce that the two unknown angles is 60, 60, making the triangle ROU an equilateral triangle.
All sides are equal in an equilateral triangle, therefore, RU = 4, Answer (D)



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
16 Oct 2017, 16:55
Bunuel wrote: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is \(\frac{4*\pi}{3}\), what is the length of line segment RU?
(A) 4/3 (B) 8/3 (C) 3 (D) 4 (E) 6
We can let the center of the circle be C. Since the radius of circle C is 4, its circumference is 2πr = 2π4 = 8π. We can use the following proportion to determine the central angle: x/360 = (4π/3)/8π x/360 = 4π/24π x/360 = 1/6 x = 60 Now triangle RUC (i.e., the triangle formed by radii RC and UC and chord RU) is at least an isosceles triangle, since RC = UC = 4. However, since x = 60 degrees, or angle RCU = 60 degrees, triangle RUC must be equilateral because angles RUC and URC are also 60 degrees. Since triangle RUC is equilateral, RU = RC = 4. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 08 Aug 2017
Posts: 6

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
20 Oct 2017, 11:03
JeffTargetTestPrep wrote: Bunuel wrote: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is \(\frac{4*\pi}{3}\), what is the length of line segment RU?
(A) 4/3 (B) 8/3 (C) 3 (D) 4 (E) 6
We can let the center of the circle be C. Since the radius of circle C is 4, its circumference is 2πr = 2π4 = 8π. We can use the following proportion to determine the central angle: x/360 = (4π/3)/8π x/360 = 4π/24π x/360 = 1/6 x = 60 Now triangle RUC (i.e., the triangle formed by radii RC and UC and chord RU) is at least an isosceles triangle, since RC = UC = 4. However, since x = 60 degrees, or angle RCU = 60 degrees, triangle RUC must be equilateral because angles RUC and URC are also 60 degrees. Since triangle RUC is equilateral, RU = RC = 4. Answer: D how do we know RC = UC? Thanks



Ask GMAT Experts Forum Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 963
Location: India
GPA: 3.64

The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
20 Oct 2017, 11:15
Length of arc RTU=4π/3 Angle subtended at the centre=\(\frac{4π}{3}\)/(2π*4)*360 =60 deg. In triangle RCU, radius, RC=CU=4, hence each angle is 60 deg and triangle is equilateral triangle. Hence RU=4 Answer D.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 207
Location: India
Concentration: Finance, International Business

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
19 Nov 2017, 01:51
Sorry this might seem like a silly question but why is a triangle formed here . I could find the degree measure of the and also find the length the circumference and am not understanding how to proceed further. Can someone suggest way to solve this question without assuming the triangle formed . thank you



Manager
Joined: 12 Nov 2016
Posts: 139
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39 GMAT 2: 650 Q47 V33

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
21 Nov 2017, 10:11
Why make a life harder and resolve via a triangle? I got another comment  in this type of questions it is likely that a triangle is equilateral otherwise it would be too difficult to find the line segment, right? Wouldn't it be safe to assume so?



Director
Joined: 09 Mar 2016
Posts: 940

Re: The points R, T, and U lie on a circle that has radius 4. If
[#permalink]
Show Tags
15 Apr 2018, 07:04
Bunuel wrote: SOLUTION
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is \(\frac{4*\pi}{3}\), what is the length of line segment RU?
(A) 4/3 (B) 8/3 (C) 3 (D) 4 (E) 6
The circumference of a circle=\(2*\pi*r=8*\pi\), \(\frac{RTU}{8*\pi}= \frac{(\frac{4*\pi}{3})}{8\pi}=\frac{1}{6}\). > Angle \(\angle{RCU}=\frac{360}{6}=60\) degrees (C center of the circle).
RCU is isosceles triangle as \(RC=CU=r\) and \(RCU=CRU=CUR=60\) degrees. Hence \(RU=r=4\).
Answer: D. Bunuel hello How do you visuilize in mind and understand that we talk about triangle let alone isolosces ? please explain:)




Re: The points R, T, and U lie on a circle that has radius 4. If &nbs
[#permalink]
15 Apr 2018, 07:04






