If PQRO is a square inside a Circle with centre at "O" and : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 00:24

### 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

# If PQRO is a square inside a Circle with centre at "O" and

Author Message
TAGS:

### Hide Tags

Manager
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 72
GMAT Date: 10-01-2012
Followers: 3

Kudos [?]: 65 [0], given: 84

If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

16 Sep 2012, 02:17
4
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

88% (02:41) correct 12% (01:53) wrong based on 91 sessions

### HideShow timer Statistics

Attachment:

Image.png [ 3.12 KiB | Viewed 1783 times ]
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C. a^2((9pi-16)/12)
D. a((3pi-1)/12)
E. a^2/11
[Reveal] Spoiler: OA

_________________

I will rather do nothing than be busy doing nothing - Zen saying

Senior Manager
Joined: 15 Jun 2010
Posts: 368
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 11

Kudos [?]: 369 [0], given: 50

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

16 Sep 2012, 02:26
1
This post was
BOOKMARKED
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 892 [1] , given: 43

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

16 Sep 2012, 05:26
1
KUDOS
1
This post was
BOOKMARKED
SOURH7WK wrote:
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)

Just a remark: For any quadrilateral with perpendicular diagonals (so obviously also for a square), the area is given by half the product of the diagonals.
(You can easily deduce it by expressing the areas of the triangles formed by the diagonals.)

So, when you know the diagonal of a square, you don't have to compute the side in order to find the area. You just have to square the diagonal and half it.
In the given question, the diagonal of the square is $$a$$ (the radius of the circle), so the area of the square is $$a^2/2.$$
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 07 Jan 2013
Posts: 26
Location: Poland
GPA: 3.8
Followers: 0

Kudos [?]: 7 [0], given: 491

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

13 Nov 2013, 13:57
SOURH7WK wrote:
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11

So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)

???? my answer is a square (a square (pi -1)/4) or asquare pi - 4 a square.!!!
Current Student
Joined: 03 Jan 2013
Posts: 186
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 750 Q48 V46
GPA: 3.02
WE: Engineering (Other)
Followers: 2

Kudos [?]: 27 [0], given: 0

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

14 Nov 2013, 06:45
Area of one quarter of the circle: (pi*a^2)/4

Area of the square:

Diagonal is equal to radius a. Therefore s(sqrt2) = a --> s = a/(sqrt2)
s^2 = (a^2)/2

Area of the shaded region is area of one quarter of the circle minus area of the square:

(pi*a^2)/4 - (a^2)/2 = [(pi*a^2) - 2(a^2)]/4

Factor out a^2:

a^2[(pi-2)/4]

Intern
Joined: 15 Jul 2012
Posts: 43
Followers: 0

Kudos [?]: 13 [0], given: 7

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

09 May 2015, 01:36
Devon wrote:
Area of one quarter of the circle: (pi*a^2)/4

Area of the square:

Diagonal is equal to radius a. Therefore s(sqrt2) = a --> s = a/(sqrt2)
s^2 = (a^2)/2

Area of the shaded region is area of one quarter of the circle minus area of the square:

(pi*a^2)/4 - (a^2)/2 = [(pi*a^2) - 2(a^2)]/4

Factor out a^2:

a^2[(pi-2)/4]

You have reduced qone quadrant with area of Square, I am fine with it. But I have worked out complete Area of circle minus Area of Square which gives= a^2(Pi-1/2). What is wrong in this?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13494
Followers: 576

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

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

08 Jun 2016, 07:20
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.
_________________
Senior Manager
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 435
GPA: 2.81
Followers: 66

Kudos [?]: 810 [0], given: 220

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

### Show Tags

08 Jun 2016, 09:20
Pansi wrote:
Attachment:
Image.png
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?

A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C. a^2((9pi-16)/12)
D. a((3pi-1)/12)
E. a^2/11

OQ=a,So OR=$$\frac{a}{\sqrt{2}}$$,So area of the Square=($$\frac{a}{\sqrt{2}}$$)^2=$$\frac{a^2}{2}$$

OQ=a,So area of the $$\frac{1}{4}$$th of the Circle=$$\pi$$$$a^2$$/4

So the area of the shaded portion=($$\pi$$$$a^2$$/4)-$$\frac{a^2}{2}$$=$$a^2$$($$\pi$$-2/4)

_________________

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Re: If PQRO is a square inside a Circle with centre at "O" and   [#permalink] 08 Jun 2016, 09:20
Similar topics Replies Last post
Similar
Topics:
If the radius of the circle with centre O is 7 and the measure of angl 3 18 May 2016, 01:12
1 In the figure above, the circle with center O is inscribed inside squa 6 03 Jan 2016, 12:09
2 In the figure above, a circle with center O is inscribed in the square 5 26 Dec 2014, 07:31
1 A circle with centre O is inscribed in a square whose side is 6 1 10 Sep 2014, 00:48
8 If circle O is inscribed inside of equilateral triangle T, w 5 12 Jan 2014, 19:19
Display posts from previous: Sort by