Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU? A. 4/3 B. 8/3 C. 3 D. 4 E. 6

this one might be easy.. but i am not able to figure it out..

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 \(RU=r=4\).

Let's call the center of the circle O; we then have a triangle ORU. Notice that OR and OU are both a radius, so they are equal in length, so this triangle must be isosceles, and the angles at R and U must be equal.

The circumference of the circle is 8*Pi. So if arc RTU is 4*Pi/3, then arc RTU is 1/6th of the circle. Thus the angle ORU is 1/6th of 360 degrees, so is 60 degrees. Now the angles at R and U must be equal, and since the angles in this triangle must add to 180, the angles at R and U must both be 60 degrees. So ORU is in fact equilateral, and every side is 4 long.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU? A. 4/3 B. 8/3 C. 3 D. 4 E. 6

this one might be easy.. but i am not able to figure it out..

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 if I follow you correctly RCU is 60 degrees because the arc RTU is 1/6 of the circumference so RCU is the central angle and will have the same measure as the arc.

Secondly since RCU=60 degrees as RC and CU are both equal we need to have 180 degrees total in the triangle so we have 120 remaining which is divided by two indicating that all 3 lines have a length of 4? Please advise. thanks.

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU? A. 4/3 B. 8/3 C. 3 D. 4 E. 6

this one might be easy.. but i am not able to figure it out..

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 if I follow you correctly RCU is 60 degrees because the arc RTU is 1/6 of the circumference so RCU is the central angle and will have the same measure as the arc.

Secondly since RCU=60 degrees as RC and CU are both equal we need to have 180 degrees total in the triangle so we have 120 remaining which is divided by two indicating that all 3 lines have a length of 4? Please advise. thanks.

Yes. From RC=CU=r and <RCU=60 we can get that triangle RCU is equilateral.
_________________

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU? A. 4/3 B. 8/3 C. 3 D. 4 E. 6

this one might be easy.. but i am not able to figure it out..

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.

Can you give me the geometric logic of finding angle RCU (360/6) _________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*PI/3, what is the length of line segment RU? A. 4/3 B. 8/3 C. 3 D. 4 E. 6

this one might be easy.. but i am not able to figure it out..

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.

Can you give me the geometric logic of finding angle RCU (360/6)

Arc RTU is 60 degrees, thus the central angle RCU, which subtends it, is also 60 degrees (a central angle in a circle determines an arc).
_________________

Re: The points R, T, and U lie on a circle that has radius 4 [#permalink]

Show Tags

15 Aug 2015, 04:44

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: The points R, T, and U lie on a circle that has radius 4 [#permalink]

Show Tags

16 Oct 2016, 12:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: The points R, T, and U lie on a circle that has radius 4 [#permalink]

Show Tags

22 Oct 2016, 23:13

We know that length of an arc = Perimeter of a circle * ( Angle subtended at the center by the arc/360)

Perimeter can be found by = 2* Pi* R = 8 * Pi

Utilizing arc length formula Perimeter of a circle * ( Angle subtended at the center by the arc/360) = 4* Pi /3

=> 8 * Pi * ( Angle subtended at the center by the arc/360) = 4* Pi /3 =>Angle subtended at the center by the arc = 60 degrees

Now, end points at circle R & U will be equidistant from center of the circle = radius of circle , r = 4 We have a triangle where one angle is 60 and two sides equal . the triangle becomes an equilateral triangle.

Re: The points R, T, and U lie on a circle that has radius 4 [#permalink]

Show Tags

23 Oct 2016, 00:58

use the ratio \(\frac{x}{360} = \frac{Arc RTU}{2*Pi*R}\) Then you find that x=60° Given that ORU is an isosceles triangle (0 is the centre of the circle), you have all angle = 60° therefore, the triangle is equilateral, the length of RU = R = 4