It is currently 25 Jun 2017, 04:14

### 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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Sep 2010
Posts: 53
ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

17 Apr 2011, 00:04
11
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:54) correct 46% (02:19) wrong based on 120 sessions

### HideShow timer Statistics

ABCD is a rectangle inscribed in a circle.
[Reveal] Spoiler: OA

Attachments

geo.png [ 24.52 KiB | Viewed 3706 times ]

_________________

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

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

17 Apr 2011, 00:36
3
KUDOS
annmary wrote:
hello
i cant solve this geometry question , plz help!
tanx

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"
_________________
Manager
Joined: 18 Sep 2010
Posts: 53
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

17 Apr 2011, 06:12
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

Manager
Joined: 18 Jan 2011
Posts: 230
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

17 Apr 2011, 14:20
1
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!!!****

Senior Manager
Joined: 08 Nov 2010
Posts: 408
WE 1: Business Development
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

19 Apr 2011, 05:47
7
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.
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 408
WE 1: Business Development
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

19 Apr 2011, 06:07
thanks old friend.
_________________
Manager
Joined: 09 Jan 2010
Posts: 125
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

01 May 2011, 20:10
1
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.
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1326
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

01 May 2011, 22:29
1
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
Joined: 09 Sep 2013
Posts: 15964
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

25 Apr 2015, 21:53
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.
_________________
Intern
Joined: 03 Jul 2015
Posts: 10
Location: India
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

19 Jul 2015, 00:34
2
KUDOS
annmary wrote:
ABCD is a rectangle inscribed in a circle.

Rectangle $$ABCD$$ can be broken down into 2 congruent triangles, $$\triangle$$$$ABC$$ & $$\triangle$$$$CDA$$.

area of rectangle $$ABCD$$ = 2 * area of $$\triangle$$$$ABC$$

Let's draw a perpendicular from B to AC and denote the length by h.

Also, $$AC = 2r = 2$$

Now, area of $$\triangle$$$$ABC$$ $$= (1/2)*(2)*(h) = h$$

area of rectangle $$ABCD = 2h$$

Now maximum value of h can be r and minimum can be tending towards 0.

So, area of rectangle will vary between $$0$$ and $$2$$.

$$Answer D$$
Manager
Joined: 03 May 2013
Posts: 75
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

17 Oct 2015, 00:27
15 seconds solution
the max area of a rectangle could be the area of squire that can be inscribed in circle with vertices on edges of circle , hence max area could be 2*2 / 2 as 2 is the max length of dignol of squire, hence D
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15964
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

26 Mar 2017, 23:25
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.
_________________
Intern
Joined: 05 Dec 2016
Posts: 7
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr [#permalink]

### Show Tags

05 May 2017, 07:26
Trigonometric Approach

Since the radius is equal to 1, the diagonal of rectangle is equal to 2r = 2

Consider angle CAD = x

Hence CD= 2 sin x and AD= 2 cos x

Area of the rectangle ABCD= AD.CD = (2sinx)(2cosx)= 2(2sinx.cosx) = 2 sin 2x

Now sin2x has maximum value 1 & minimum value 0

Hence 0 < area (ABCD) < 2

Therefore OPTION D
Re: ABCD is a rectangle inscribed in a circle. If the length of AB is thr   [#permalink] 05 May 2017, 07:26
Similar topics Replies Last post
Similar
Topics:
9 The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of 5 02 Feb 2016, 11:38
8 In the figure above, ABCD is a rectangle inscribed in a circle. Angle 8 27 Mar 2017, 10:18
4 In the figure above, ABCD is a rectangle inscribed in a circle. If the 7 25 May 2017, 19:01
13 Rectangle ABCD is inscribed in a circle with center X. If the area of 9 28 Apr 2017, 03:02
7 Rectangle ABCD with a perimeter of 60 is inscribed in a circle with a 4 27 Mar 2017, 10:24
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.