What is the circumference of the circle above with center O? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 12:17

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the circumference of the circle above with center O?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2329 [0], given: 0

What is the circumference of the circle above with center O? [#permalink]

### Show Tags

26 Dec 2012, 03:59
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:53) correct 20% (01:13) wrong based on 643 sessions

### HideShow timer Statistics

Attachment:

Circle.png [ 10.62 KiB | Viewed 10760 times ]
What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$.
(2) The length of arc XYZ is $$5\pi$$.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93346 [1] , given: 10557

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

26 Dec 2012, 04:05
1
KUDOS
Expert's post
4
This post was
BOOKMARKED

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

_________________
Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1045 [0], given: 543

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

12 Jan 2013, 07:33
Bunuel wrote:

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

Is there a formula for this explanation?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93346 [0], given: 10557

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

13 Jan 2013, 02:29
fozzzy wrote:
Bunuel wrote:

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

Is there a formula for this explanation?

Yes, check here: math-circles-87957.html (see Arc Length under Arcs and Sectors chapter)
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13485
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

02 Jan 2015, 06:56
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8307
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 381

Kudos [?]: 2467 [1] , given: 163

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

02 Jan 2015, 13:06
1
KUDOS
Expert's post
Hi All,

Even though this DS question is about Geometry rules, it involves a great Algebra shortcut that you'll see at least once on Test Day.

We're given a circle with an ISOSCELES right triangle within it (with the 3 vertices at the center of the circle and on the circumference), so we have a 45/45/90 right triangle. We're asked for the circumference of the circle.

Fact 1: The perimeter of triangle OXZ = 20 + 10\sqrt{2}

Since the triangle is a 45/45/90, we know the sides are A, A and A\sqrt{2}, thus...

A + A + A\sqrt{2} = 20 + 10\sqrt{2}

We have ONE VARIABLE and ONE equation, so we CAN solve it (and since there are no additional possible answers, re. due to exponents, absolute values, etc. - there will be JUST ONE ANSWER.)
Fact 1 is SUFFICIENT.

Fact 2: Arc XYZ = 5pi

Since this arc is based on a 90 degree angle, we CAN figure out what fraction of the circumference we're dealing with (it's 1/4, but that math is not necessary). In this way we have the SAME shortcut that we had in Fact 1: ONE VARIABLE and ONE equation, so we CAN solve it.
Fact 2 is SUFFICIENT.

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13485
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: What is the circumference of the circle above with center O? [#permalink]

### Show Tags

02 Jan 2017, 14:32
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: What is the circumference of the circle above with center O?   [#permalink] 02 Jan 2017, 14:32
Similar topics Replies Last post
Similar
Topics:
1 What is the circumference of circle O? 8 23 Jun 2016, 01:06
What is the area of the circle above with center O? 4 27 Dec 2015, 09:56
1 In the diagram above, O is the center of the circle. What is the leng 5 11 Mar 2015, 03:47
6 What is the radius of the circle above with center O? 9 26 Jan 2014, 09:42
What is the area of the circle above with center O. 2 01 May 2013, 04:32
Display posts from previous: Sort by