It is currently 17 Oct 2017, 08:28

### 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

# The Quadrilateral shown above is a square. Four circles are

Author Message
TAGS:

### Hide Tags

Intern
Joined: 12 Feb 2013
Posts: 6

Kudos [?]: 19 [1], given: 18

### Show Tags

26 Apr 2013, 12:12
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

61% (01:53) correct 39% (02:38) wrong based on 96 sessions

### HideShow timer Statistics

The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)
[Reveal] Spoiler: OA

Attachments

Untitled.png [ 10.2 KiB | Viewed 2422 times ]

Kudos [?]: 19 [1], given: 18

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2325 [2], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

### Show Tags

26 Apr 2013, 12:39
2
KUDOS
alex90 wrote:
The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)

Lets assume that the radius of the big circle is 1.
Create a square connecting all the centers (look picture). Its side is 2, it diagonal is $$2\sqrt{2}$$, this if formed by 2 radius and the diameter of the smaller circle
$$2\sqrt{2}-2(=2*radiusBig)=diameterSmall$$ $$2(\sqrt{2}-1)=diamSmall$$
so radius small = $$\sqrt{2}-1$$

The ratio radius to side square (= 4) is $$(\sqrt{2}-1)/4$$
B
Attachments

Untitled.png [ 7.87 KiB | Viewed 2375 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2325 [2], given: 219

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [0], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

### Show Tags

26 Apr 2013, 15:45
alex90 wrote:
The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)

Is this question copied from the OG verbatim?

The section I highlighted in red seems to fail to aknowledge what ratio they asking (diameter of small circle vs side of square? Circumference of circle vs side of square? etc)

Kudos [?]: 15 [0], given: 0

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2615 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

### Show Tags

29 Apr 2013, 02:45
I considered it as ratio of radius of small circle to the side of the square (yes, the question lacks clarity as to what ratio asked for)

Considering 2 as side of the square

(sqrt2 - 1)/2 = Radius of small circle
2 = Side of Square;Solving it further, we get ans = 1/(4.sqrt2-1)
_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2615 [0], given: 193

VP
Joined: 09 Jun 2010
Posts: 1403

Kudos [?]: 158 [0], given: 916

Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

### Show Tags

01 May 2015, 03:11
the wording of this problem is bad. it is not from og.

ok, the concept tested is simple.
_________________

visit my facebook to help me.
on facebook, my name is: thang thang thang

Kudos [?]: 158 [0], given: 916

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16762

Kudos [?]: 273 [0], given: 0

Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

### Show Tags

14 Nov 2016, 12:32
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: The Quadrilateral shown above is a square. Four circles are   [#permalink] 14 Nov 2016, 12:32
Display posts from previous: Sort by