GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Aug 2019, 04:39

### GMAT Club Daily Prep

#### 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

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

# The circle with center O has a circumference of 6π

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57191
The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

16 Jun 2015, 03:28
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:53) correct 27% (02:11) wrong based on 186 sessions

### HideShow timer Statistics

The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

(A) $$\frac{3}{\sqrt{2}}$$

(B) 3

(C) $$3\sqrt{3}$$

(D) 9

(E) $$9\sqrt{3}$$

Kudos for a correct solution.
Attachment:

2015-06-16_1428.png [ 17.41 KiB | Viewed 4607 times ]

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

16 Jun 2015, 05:22
1
Bunuel wrote:

The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

(A) $$\frac{3}{\sqrt{2}}$$

(B) 3

(C) $$3\sqrt{3}$$

(D) 9

(E) $$9\sqrt{3}$$

Kudos for a correct solution.
Attachment:
2015-06-16_1428.png

Circumference of Circle = $$6\pi{\sqrt{3}}$$ = $$2\pi{r}$$ where r is the radius of circle

i.e. $$r = 3{\sqrt{3}}$$ = AC/2

Since, Side AC of Triangle is equal to the Diameter therefore Angle ABC must be 90 degree

CONCEPT: Angle drawn in a semicircle on the circumference is always 90 degrees

i.e. Triangle ABC is 30-60-90 Traingle with ratio of the sides $$x:x{\sqrt{3}}:2x$$

and AC = $$2x = 2r = 6{\sqrt{3}}$$

therefore, BC = $$x{\sqrt{3}} = 3{\sqrt{3}}*{\sqrt{3}}$$

i.e. BC = 9

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 19 Jan 2014
Posts: 20
Concentration: Marketing, Economics
GPA: 3.81
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

16 Jun 2015, 06:48
2
Circumference of a circle = 2$$\pi$$r = 6$$\pi\sqrt{3}$$
This means r(radius)= 3$$\sqrt{3}$$
AC= diameter= 2r = 6$$\sqrt{3}$$

In triangle ABC,
cos 30 = $$\frac{BC}{AC}$$
$$\sqrt{3}$$/2 = BC/6$$\sqrt{3}$$
BC= 9

Option D
Intern
Joined: 08 Sep 2014
Posts: 25
GMAT Date: 07-11-2015
GPA: 2.9
WE: Account Management (Computer Software)
The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

Updated on: 16 Jun 2015, 14:01
Bunuel wrote:

The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

(A) $$\frac{3}{\sqrt{2}}$$

(B) 3

(C) $$3\sqrt{3}$$

(D) 9

(E) $$9\sqrt{3}$$

Kudos for a correct solution.
Attachment:
2015-06-16_1428.png

This is a 30-60-90 triangle and we are told that the circumference is $$6\pi{\sqrt{3}}$$. Set $$6\pi{\sqrt{3}}$$ = $$2(\pi)r$$ giving you r = $$3{\sqrt{3}}$$

You know the diameter, line AC equal 2r or $$6{\sqrt{3}}$$

If you remember your 30-60-90 angles, you can calculate the 60 degree angle, $$3{\sqrt{3}}$$*$${\sqrt{3}}$$ BC = 9

Originally posted by BuggerinOn on 16 Jun 2015, 08:14.
Last edited by BuggerinOn on 16 Jun 2015, 14:01, edited 2 times in total.
Manager
Joined: 26 Dec 2011
Posts: 115
Schools: HBS '18, IIMA
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

16 Jun 2015, 10:36
1
The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

Solution -

Angle B is always 90 degrees. So C=30 and A=60.

Triangle ABC is 30-60-90 Triangle with ratio of the sides x:x√3:2x.

2$$\pi$$r=$$6\pi{\sqrt{3}}$$ ->Diameter(2r) = AC = 2x = 6√3 ->x=3√3.

BC = x√3 = 9. ANS D.

Thanks,

_________________
Thanks,
Retired Moderator
Joined: 29 Apr 2015
Posts: 826
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

16 Jun 2015, 11:20
1
Bunuel wrote:

The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

(A) $$\frac{3}{\sqrt{2}}$$

(B) 3

(C) $$3\sqrt{3}$$

(D) 9

(E) $$9\sqrt{3}$$

Kudos for a correct solution.

Attachment:
2015-06-16_1428.png

Inscribed triangle ABC is a 30-60-90 triangle. Angle ABC = 90 because the opposite line is the diameter of the Circle. Angle CAB is 60 to add up to a Total of 180 Degrees.

AC = Diameter of the Circle = $$6\sqrt{3}$$ which equals 2x in the special right triangle. Solve for x by dividing by 2: $$3\sqrt{3}$$ = x. Finally BC = $$x\sqrt{3}$$ = $$3\sqrt{3}*\sqrt{3}$$=9

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
Math Expert
Joined: 02 Sep 2009
Posts: 57191
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

22 Jun 2015, 06:49
Bunuel wrote:

The circle with center O has a circumference of $$6\pi{\sqrt{3}}$$. If AC is a diameter of the circle, what is the length of line segment BC?

(A) $$\frac{3}{\sqrt{2}}$$

(B) 3

(C) $$3\sqrt{3}$$

(D) 9

(E) $$9\sqrt{3}$$

Kudos for a correct solution.
Attachment:
The attachment 2015-06-16_1428.png is no longer available

MANHATTAN GMAT OFFICIAL SOLUTION:

Some intuitive recollection of geometry rules and a picture drawn to scale can help us determine reasonable answer choices. If AC is a diameter of the circle, then triangle ABC is a right triangle, with angle ABC = 90 degrees. The shortest side of a triangle is across from its smallest angle, and the longest side of a triangle is across from its largest angle. Therefore, AC > BC > AB.

The circumference of the circle = $$\pi{d}=6\pi{\sqrt{3}}$$, so $$d=6\sqrt{3}\approx{6*1.7}=10.2$$ Thus, AC ≈ 10.2 and BC < 10.2. But we can clearly see from our picture drawn to scale that BC is longer than half the diameter, so we conservatively determine that BC > 5.1.

Attachment:

2015-06-22_1748.png [ 37.46 KiB | Viewed 4182 times ]

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 12052
Re: The circle with center O has a circumference of 6π  [#permalink]

### Show Tags

04 Aug 2019, 21:51
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 circle with center O has a circumference of 6π   [#permalink] 04 Aug 2019, 21:51
Display posts from previous: Sort by