Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 20:06

Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A circle is inscribed in a quadrant of a circle of radius 1

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [1] , given: 235

GMAT Tests User Reviews Badge
A circle is inscribed in a quadrant of a circle of radius 1 [#permalink] New post 07 Mar 2010, 12:20
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (01:11) correct 33% (01:13) wrong based on 2 sessions
A circle is inscribed in a quadrant of a circle of radius 1 unit. What is the area of the shaded region?

I donot have the options and ans, but we can have discussion over this.

PS: This is a difficult question and might not be tested in GMAT, but solving such questions might help us learning new concept.

DISCUSSED HERE: consider-a-quarter-of-a-circle-of-radius-16-let-r-be-the-131083.html
Attachments

1.jpg
1.jpg [ 8.45 KiB | Viewed 7880 times ]


_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html


Last edited by gurpreetsingh on 07 Mar 2010, 13:41, edited 1 time in total.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 365
Followers: 10

Kudos [?]: 199 [1] , given: 47

GMAT ToolKit User GMAT Tests User
Re: geometry - circles [#permalink] New post 07 Mar 2010, 13:07
1
This post received
KUDOS
gurpreetsingh wrote:
I donot have the options and ans, but we can have discussion over this.


Wild Spin!!! :maniac

I am able to take out the area of the inscribed circle... after that am lost...!
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [1] , given: 235

GMAT Tests User Reviews Badge
Re: geometry - circles [#permalink] New post 07 Mar 2010, 13:15
1
This post received
KUDOS
Shar your steps, toghther we might solve.

one of my teacher once told me, 2 fools can solve any problem...lol
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 365
Followers: 10

Kudos [?]: 199 [2] , given: 47

GMAT ToolKit User GMAT Tests User
Re: geometry - circles [#permalink] New post 07 Mar 2010, 13:30
2
This post received
KUDOS
gurpreetsingh wrote:
Shar your steps, toghther we might solve.

one of my teacher once told me, 2 fools can solve any problem...lol


hahaha... :D

Let the radius of the smaller circle be r... and let the distance from center of bigger circle to the circumference of inscribed circle be x. Check the figure.

2r + x = 1

x + r = \sqrt{2}r
Therefore x = (\sqrt{2} - 1)r

Therefore 2r + (\sqrt{2} - 1)r = 1
Which gives r = (\sqrt{2} - 1)

Now you can find the area of the smaller circle....

This is the limit, this fool can reach! :lol: All over to the other fool! :wink:
Attachments

Circle.png
Circle.png [ 16.19 KiB | Viewed 7834 times ]


_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [0], given: 235

GMAT Tests User Reviews Badge
Re: geometry - circles [#permalink] New post 07 Mar 2010, 13:40
lol i think its solved.

Shaded portion = Area of sector 1 - area of triangle 1 - area of sector 2

where area of sector 1 = area made by 45 degree of bigger circle.

area of triangle 1 is where you have applied Pythagoras theorem

area of sector 2 = area made by 135 degree of smaller circle.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 365
Followers: 10

Kudos [?]: 199 [0], given: 47

GMAT ToolKit User GMAT Tests User
Re: geometry - circles [#permalink] New post 07 Mar 2010, 14:13
gurpreetsingh wrote:
lol i think its solved.

Shaded portion = Area of sector 1 - area of triangle 1 - area of sector 2

where area of sector 1 = area made by 45 degree of bigger circle.

area of triangle 1 is where you have applied Pythagoras theorem

area of sector 2 = area made by 135 degree of smaller circle.


Cool!!!! :good Do they allow two fools together in GMAT :) :lol
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [0], given: 235

GMAT Tests User Reviews Badge
Re: geometry - circles [#permalink] New post 07 Mar 2010, 20:55
Its all about team work, Gmat should also be flexible.

I will find my partner to be good in verbal and then atleast i can think of 700+
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 56

Kudos [?]: 457 [0], given: 157

GMAT ToolKit User GMAT Tests User
Re: geometry - circles [#permalink] New post 25 Apr 2010, 02:05
One query,, how did jeteesh derive the following equation.

x+r=\sqrt{2}r

I am struck.
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [0], given: 235

GMAT Tests User Reviews Badge
Re: geometry - circles [#permalink] New post 25 Apr 2010, 04:32
Hussain15 wrote:
One query,, how did jeteesh derive the following equation.

x+r=\sqrt{2}r

I am struck.


Just look at the right angled triangle whose 2 sides are r and hypotenuse is x+r

=>(x+r)^2 = r^2 +r^2

=> x+r = \sqrt{2}r

Here x is basically the distance from the center of bigger circle to the smaller circle.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 20 Apr 2010
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: geometry - circles [#permalink] New post 27 Apr 2010, 13:22
How does the first equation can turn to the second one?
2r + (\sqrt{2} - 1)r = 1
r = (\sqrt{2} - 1)
Manager
Manager
avatar
Joined: 29 Dec 2009
Posts: 122
Location: india
Followers: 1

Kudos [?]: 13 [0], given: 10

GMAT Tests User
Re: geometry - circles [#permalink] New post 30 Apr 2010, 11:05
if v can extend the figure like take big circle ... then put in 4 circles of (root2 -1) radius in it.... then joining the centres of four circles v will form a square with an area = (2(root2 -1))^2 coz radiu smaller circles is root2 -1 ..... then to get the shaded region

= {area of big circle - {3(area of smaller circle) + (2(root2 -1))^2}} / 8 ...... v subtracted three circles coz i circle ia in the square.. :?:
Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 60
Followers: 2

Kudos [?]: 17 [0], given: 303

Re: geometry - circles [#permalink] New post 06 May 2011, 00:46
area of small circle is=\pi{r^2}=\pi*(\sqrt{2} - 1)^2
area of Quarter=(\pi*{1^2})/4=\pi/4.
area of shaded region=(\pi/4-\pi*(\sqrt{2} - 1)^2 -(r^2-1/4(\pi*(\sqrt{2} - 1)^2)) / 2

Last edited by annmary on 06 May 2011, 07:43, edited 2 times in total.
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 10

Kudos [?]: 132 [0], given: 10

GMAT Tests User
Re: geometry - circles [#permalink] New post 06 May 2011, 06:11
the bigger radius comes out to be = 1 + 2^(1/2).
So from the sector Area,subtract the circle area and the area of the sector between circle and edge of the bigger sector

the area of the edge sector = 1- pi/4

thus the shaded region area can be found out.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Intern
Intern
avatar
Joined: 29 Aug 2011
Posts: 24
Followers: 1

Kudos [?]: 4 [0], given: 3

Re: geometry - circles [#permalink] New post 01 Sep 2012, 12:14
Looking for complete solution with good explanation. I could reach half of the solution.
Intern
Intern
avatar
Joined: 28 Aug 2012
Posts: 48
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 29 [0], given: 3

Re: geometry - circles [#permalink] New post 01 Sep 2012, 13:11
area of Quarter of big circle=(\pi*{1^2})/4=\pi/4.
The radius r of the inscribed smaller circle: r = \sqrt{2} - 1
See explanation for this above.

Area not covered by small circle = \pi/4-\pi*(\sqrt{2} - 1)^2

Small area in the corner (near center of big circle) not covered by small circle:
Small square (see picture above) - a quarter of the smaller circle
(\sqrt{2} - 1)^2-\pi*(\sqrt{2} - 1)^2/4

Area not covered by small circle and not including the small area in the corner:
\pi/4-\pi*(\sqrt{2} - 1)^2-((\sqrt{2} - 1)^2-\pi*(\sqrt{2} - 1)^2/4)

This area now represents the shaded area upper left and its mirror area bottom right. So we only have to divide by 2 to get the area of the shaded area.
(\pi/4-\pi*(\sqrt{2} - 1)^2-((\sqrt{2} - 1)^2-\pi*(\sqrt{2} - 1)^2/4))/2 = 0.10478
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18856
Followers: 3275

Kudos [?]: 22916 [0], given: 2651

Re: A circle is inscribed in a quadrant of a circle of radius 1 [#permalink] New post 03 Sep 2012, 04:39
Expert's post
Re: A circle is inscribed in a quadrant of a circle of radius 1   [#permalink] 03 Sep 2012, 04:39
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If a regular hexagon is inscribed in a circle with a radius fozzzy 7 02 Jun 2013, 00:38
59 Experts publish their posts in the topic A rectangle is inscribed in a circle of radius r. If the alex1233 31 16 May 2012, 06:44
2 Circle Inscribed in a triangle-radius ? soaringAlone 7 15 Jun 2011, 20:43
2 Regular hexagon is inscribed in a circle. If the radius of t bigfernhead 6 28 Jan 2009, 15:44
A rectangle is inscribed in a circle whose radius equals R. drdas 3 03 Oct 2004, 08:41
Display posts from previous: Sort by

A circle is inscribed in a quadrant of a circle of radius 1

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.