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

It is currently 04 Jul 2015, 00:44

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

ABCD is a rectangle inscribed in a circle. If the length of AB is thr

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 53
Followers: 2

Kudos [?]: 22 [0], given: 303

ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 16 Apr 2011, 23:04
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

39% (03:15) correct 61% (02:43) wrong based on 23 sessions
ABCD is a rectangle inscribed in a circle.
[Reveal] Spoiler: OA

Attachments

geo.png
geo.png [ 24.52 KiB | Viewed 2195 times ]


_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

3 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2028
Followers: 138

Kudos [?]: 1163 [3] , given: 376

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 16 Apr 2011, 23:36
3
This post received
KUDOS
annmary wrote:
hello
i cant solve this geometry question :shock: , plz help!
tanx :oops:


Sol:
Let l=length
w=wdith
d=diagonal=2
\(Area=l*w=l*\sqrt{d^2-l^2}\)

\(l*\sqrt{2^2-l^2}\)

\(l*\sqrt{4-l^2}=Area\)

Squaring both sides;
\(l^2*(4-l^2)=(Area)^2\)
\(4l^2-l^4=(Area)^2\)
\(-l^4+4l^2-(Area)^2=0\)

\(Let \hspace{2} l^2=x\)

\(-x^2+4x-(Area)^2=0\)

\(D=\sqrt{b^2-4*a*c}\)

\(D=\sqrt{4^2-4*(-1)*-(Area)^2}\)

\(D=\sqrt{16-4*(Area)^2}\)

In inside of the root must be greater or equal to 0 to provide valid roots of the equation.
\(16-4*(Area)^2 \ge 0\)

\(4*(Area)^2 \le 16\)

\((Area)^2 \le 4\)

\((Area) \le 2\)

Only I and II are less than 2.

Ans: "D"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 53
Followers: 2

Kudos [?]: 22 [0], given: 303

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 17 Apr 2011, 05:12
thank you fluke
your solution is very well.
+5 kudos , but i just can give you +1 kudos ;-)
other 4 kudos :+1,+1,+1,+1
_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Jan 2011
Posts: 231
Followers: 1

Kudos [?]: 26 [1] , given: 4

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 17 Apr 2011, 13:20
1
This post received
KUDOS
1
This post was
BOOKMARKED
Area cannot be 3.2 because area of circle is pi r^2 i.e. 3.14, so rule out III
Even if the length is very close to the diameter i.e. 1 approx, width has to be 1/100 to make the area .01 - possible
similarly 1.9 is also possible.
=>D
_________________

Good Luck!!!

***Help and be helped!!!****

5 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 419
WE 1: Business Development
Followers: 7

Kudos [?]: 54 [5] , given: 161

GMAT ToolKit User
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 19 Apr 2011, 04:47
5
This post received
KUDOS
i did it a bit different.

Max size for a rectangle is a square.
and minimum is when the width or length = to 0 (or almost 0)

so lets check the max and than we know that everything below the max is a possibility.

so if we know the radii is 1 - we know that if it was a square its diagonals will be 2 each.
so the area of the rectangle will be < 2*2/2 = 2

so - I, II is below 2, above 0 - than - they are ok.
_________________

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 419
WE 1: Business Development
Followers: 7

Kudos [?]: 54 [0], given: 161

GMAT ToolKit User
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 19 Apr 2011, 05:07
thanks old friend.
_________________

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Manager
Manager
avatar
Joined: 09 Jan 2010
Posts: 128
Followers: 1

Kudos [?]: 7 [1] , given: 12

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 01 May 2011, 19:10
1
This post received
KUDOS
area of rectangle = l*b

diagonal is 2
also d (diagonal) = sqrt (l^2 + b^2)
l*b = l * sqrt (2 -l^2)
area is positive
therefore (2-l^2) >0
i.e sqrt2>l
similarly sqrt2>b
therefore area = l.b <sqrt 2.sqrt2 = 1.4 *1.4 = 1.96
therefore D is correct.
1 KUDOS received
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1358
Followers: 13

Kudos [?]: 168 [1] , given: 10

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 01 May 2011, 21:29
1
This post received
KUDOS
Max area of the rectangle possible when diagonal = diameter = 2
Hence, l^2 + b^2 = 4. Implies l and b < 1.5 each.
Also, area of circle = 3.14 * 1^2 = 3.14. hence options C and E POE.
Now,
0<l <1.5 and 0<b<1.5. Thus area can be 0.01 and 1.9 both.
Hence D.
_________________

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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5364
Followers: 310

Kudos [?]: 60 [0], given: 0

Premium Member
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink] New post 25 Apr 2015, 20:53
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr   [#permalink] 25 Apr 2015, 20:53
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Rectangle ABCD is inscribed in a circle with center X. If the area of Bunuel 8 05 Feb 2015, 08:24
7 Experts publish their posts in the topic ABCD is a square inscribed in a circle and arc ADC has a length of p√x Bunuel 8 28 Oct 2014, 08:35
5 Experts publish their posts in the topic ABCD is the inscribed quadrilateral in the given circle guerrero25 4 17 Jun 2013, 12:17
77 Experts publish their posts in the topic A rectangle is inscribed in a circle of radius r. If the alex1233 37 16 May 2012, 06:44
Display posts from previous: Sort by

ABCD is a rectangle inscribed in a circle. If the length of AB is thr

  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®.