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:

In the figure above, showing circle with center O and points [#permalink]

Show Tags

25 Feb 2013, 01:21

4

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

68% (03:09) correct
32% (02:34) wrong based on 193 sessions

HideShow timer Statistics

Attachment:

1.jpg [ 5.58 KiB | Viewed 7437 times ]

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

25 Feb 2013, 03:17

3

This post received KUDOS

1

This post was BOOKMARKED

emmak wrote:

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

12

18

24

36

72

\(\angle AOB = 120^{\circ}\)

So,

\(\angle\) ACB = \(60^{\circ}\)

So, the \(\triangle\) ABC is a 30, 60, 90 triangle and the sides are in the ratio 1 : \(\sqrt{3}\) : 2

or 12 : 12\(\sqrt{3}\) : 24

So, AC = 24 and hence AO = 12

Answer is A
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Good question. It tests three must know properties for the GMAT:

1. A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

2. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

According to the above, central angle AOB is twice inscribed angle ACB (notice that both subtend the same arc AB). Hence since AOB=120 degrees (third of 360 degrees), then ACB=60 degrees. So, we have that triangle ABC is 30°-60°-90° right triangle.

3. In a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\).

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

22 May 2013, 17:38

can someone explain me why cant we use the formula arc length=2x3.14xr(c/360) we know the arc length AB and C/360 as 120..But am not getting the answer.can anyone explain why we should nt use this formula here
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

can someone explain me why cant we use the formula arc length=2x3.14xr(c/360) we know the arc length AB and C/360 as 120..But am not getting the answer.can anyone explain why we should nt use this formula here

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

24 Nov 2013, 04:44

MacFauz wrote:

emmak wrote:

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

12

18

24

36

72

\(\angle AOB = 120^{\circ}\)

So,

\(\angle\) ACB = \(60^{\circ}\)

So, the \(\triangle\) ABC is a 30, 60, 90 triangle and the sides are in the ratio 1 : \(\sqrt{3}\) : 2

or 12 : 12\(\sqrt{3}\) : 24

So, AC = 24 and hence AO = 12

Answer is A

How do you that since \(\angle AOB = 120^{\circ}\) so \(\angle\) ACB = \(60^{\circ}\) ?

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

24 Nov 2013, 10:28

Bunuel wrote:

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Good question. It tests three must know properties for the GMAT:

1. A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

2. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

According to the above, central angle AOB is twice inscribed angle ACB (notice that both subtend the same arc AB). Hence since AOB=120 degrees (third of 360 degrees), then ACB=60 degrees. So, we have that triangle ABC is 30°-60°-90° right triangle.

3. In a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\).

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

I'm having trouble visualizing your 2nd point; could you draw a rough illustration of it? I'm familiar with the theorem, great illustration here: http://www.mathopenref.com/arccentralangletheorem.html, but I can't visualize it in this problem. I got the answer correct as the sqrt(3) tipped me off to a likely 30-60-90, but I'd like to learn a bit more from this problem

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

24 Nov 2013, 15:55

AccipiterQ wrote:

Bunuel wrote:

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Good question. It tests three must know properties for the GMAT:

1. A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

2. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

According to the above, central angle AOB is twice inscribed angle ACB (notice that both subtend the same arc AB). Hence since AOB=120 degrees (third of 360 degrees), then ACB=60 degrees. So, we have that triangle ABC is 30°-60°-90° right triangle.

3. In a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\).

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

I'm having trouble visualizing your 2nd point; could you draw a rough illustration of it? I'm familiar with the theorem, great illustration here: http://www.mathopenref.com/arccentralangletheorem.html, but I can't visualize it in this problem. I got the answer correct as the sqrt(3) tipped me off to a likely 30-60-90, but I'd like to learn a bit more from this problem

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Good question. It tests three must know properties for the GMAT:

1. A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

2. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

According to the above, central angle AOB is twice inscribed angle ACB (notice that both subtend the same arc AB). Hence since AOB=120 degrees (third of 360 degrees), then ACB=60 degrees. So, we have that triangle ABC is 30°-60°-90° right triangle.

3. In a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\).

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

I'm having trouble visualizing your 2nd point; could you draw a rough illustration of it? I'm familiar with the theorem, great illustration here: http://www.mathopenref.com/arccentralangletheorem.html, but I can't visualize it in this problem. I got the answer correct as the sqrt(3) tipped me off to a likely 30-60-90, but I'd like to learn a bit more from this problem

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

08 Dec 2013, 22:26

emmak wrote:

Attachment:

1.jpg

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Guys I did this question with this approach, can you kindly evaluate the approach \(AB= \frac{1}{3} Circumference\) So,\(AB = \frac{2}{3}Pi* R\) Also \(AB=12\sqrt{3}\) Therefore, \(12\sqrt{3} = \frac{2}{3}Pi* R\) Manipulating\(R = 12\)

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

11 Dec 2013, 14:06

Ok, assuming we know this is a right triangle because we know that the picture is accurate...

If the triangle is a right triangle, we know that angle B is the right angle. Furthermore, we are given that arc AB = 1/3 of the circle's circumference (i.e it = 120 degrees) This means that AOB, the central angle = 120 degrees and because AO and BO are radii, we know that triangle AOB is an isosceles triangle. We also know the angle measure of angle BOC which = 180 - 120 = 60. If angle AOB is the interior angle, it is twice the measure of the "exterior" angle ACB, so ACB = 60. Now we know that triangle BOC is equilateral. More importantly, we know that ABC is a 30:60:90 triangle. With this, we can find the measure of any given side knowing just the measure of one. The ratio of side lengths in a 30:60:90 is (x/2):(3/2*x):(x) in this case, x (the radius) = 12.

We did not assume that. AC passes through the center of the circle thus it's the diameter.

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.
_________________

We did not assume that. AC passes through the center of the circle thus it's the diameter.

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

I understand the rule, but in other words, how do we know that the drawing isn't misleading and that AC passes above the center?

We did not assume that. AC passes through the center of the circle thus it's the diameter.

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

I understand the rule, but in other words, how do we know that the drawing isn't misleading and that AC passes above the center?

OG13, page 150: Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

OG13, page 272: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees. All figures lie in a plane unless otherwise indicated.
_________________

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

28 Jul 2014, 20:27

Bunuel wrote:

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Good question. It tests three must know properties for the GMAT:

1. A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

According to the above, we have that ABC is a right triangle, with a right angle at B.

2. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

According to the above, central angle AOB is twice inscribed angle ACB (notice that both subtend the same arc AB). Hence since AOB=120 degrees (third of 360 degrees), then ACB=60 degrees. So, we have that triangle ABC is 30°-60°-90° right triangle.

3. In a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\).

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

Particularly in this question with the given options , do we even need this much detail.

We know that the angle AOB = 120 degrees as it is 1/3 the circumference. AO=OB as they are the radius. So the two angles OAB and OBA will be equal in the triangle AOB. Thus Angle OBA=OBA=30 ( 180-120)/2. In a triangle the greatest side is opposite the largest angle . Here AB is opposite the largest angle and is 12sqrt2 so the other sides ( the radii) will have to be less that this value and only A satisfies the condition over here

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

21 Aug 2015, 23:04

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.
_________________

In the figure above, showing circle with center O and points [#permalink]

Show Tags

23 Feb 2016, 02:49

emmak wrote:

Attachment:

The attachment 1.jpg is no longer available

given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) ,

does the wording simply states that the length of the arc AB is one third WITHOUT INDICATING THE EXACT VALUE, and the value of 12 root 3 is given for the side AB (rather than the arc AB)? i think the probles is poorly worded. look how it looks in the original. veritas should not have placed that bar above AB if they meant it was not the arc but the length

Attachments

2016-02-23 16-47-01 gmat.veritasprep.com gmat exams 1105058 responses 18191158 - Google Chrome.png [ 92.84 KiB | Viewed 1933 times ]

Re: In the figure above, showing circle with center O and points [#permalink]

Show Tags

30 Jul 2016, 23:24

suk1234 wrote:

emmak wrote:

Attachment:

1.jpg

In the figure above, showing circle with center O and points A, B, and C on the circle, given that minor arc (AB) is one-third of the total circumference and length (AB)=\(12\sqrt{3}\) , what is the radius of the circle?

A. 12 B. 18 C. 24 D. 36 E. 72

Guys I did this question with this approach, can you kindly evaluate the approach \(AB= \frac{1}{3} Circumference\) So,\(AB = \frac{2}{3}Pi* R\) Also \(AB=12\sqrt{3}\) Therefore, \(12\sqrt{3} = \frac{2}{3}Pi* R\) Manipulating\(R = 12\)

AB Arc and not AB line segment is equal to 2/3 of circumference. Moreover AB arc is not 12root3, AB Line segment is.

gmatclubot

Re: In the figure above, showing circle with center O and points
[#permalink]
30 Jul 2016, 23:24

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...