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

It is currently 30 Jul 2015, 12:21
GMAT Club Tests

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

Given a quadrilateral ABCD, a circle is inscribed in the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2004
Posts: 328
Location: There
Followers: 1

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

Given a quadrilateral ABCD, a circle is inscribed in the [#permalink] New post 11 May 2004, 02:54
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 0 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Given a quadrilateral ABCD, a circle is inscribed in the quadrilateral in such a way that it touches all of the four sides. What is the perimeter of the quadrilateral?

(1) AB+BC=10
(2) AB+CD=12
1 KUDOS received
Manager
Manager
User avatar
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 9 [1] , given: 0

Re: DS-101 [#permalink] New post 11 May 2004, 03:08
1
This post received
KUDOS
hallelujah1234 wrote:
Given a quadrilateral ABCD, a circle is inscribed in the quadrilateral in such a way that it touches all of the four sides. What is the perimeter of the quadrilateral?

(1) AB+BC=10
(2) AB+CD=12


2 alone is sufficient, while 1 alone is not.

The reason behind is that for a every quadrilateral to have a circle inscribed inside it is equivalent to AB + CD = AD + BC.

Why this is so? If you mark points, where circle inscribed touches quadr. by A1, B1, C1, D1, then |AA1| = |AD1|, |BA1| = |BB1|, |CB1| = |CC1|, |DC1| = |DD1| => since AB = AA1 + BA1, BC = BB1 + CB1, CD = CC1 + DC1, DA = DD1 + AD1, AB + CD = BC + AD.

So, opposite sides of quadr. sum to equal values. => P = 2*(AB + CD) = 24.
Senior Manager
Senior Manager
avatar
Joined: 26 Jan 2004
Posts: 402
Location: India
Followers: 1

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

 [#permalink] New post 11 May 2004, 03:42
In my opinion answer should be (A),

Tangents to circle are perpendicular to the radius, using this property, we can prove that it will be a rectangle in which circle is inscribed.
Hence answer should 2*(AB+BC) = 2*10 = 20

Any comments?
Manager
Manager
User avatar
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 9 [0], given: 0

 [#permalink] New post 11 May 2004, 03:47
mba wrote:
In my opinion answer should be (A),

Tangents to circle are perpendicular to the radius, using this property, we can prove that it will be a rectangle in which circle is inscribed.
Hence answer should 2*(AB+BC) = 2*10 = 20

Any comments?


No, a quadrilateral (such that a circle can be inscribed inside it) is not always rectangle. For instance, consider romb (it has all sides equal, but its angles need not be equal to 90).

.../\.....
../..\....
..\../....
...\/.....
Intern
Intern
avatar
Joined: 21 Mar 2004
Posts: 11
Location: Evansville, IN
Followers: 0

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

 [#permalink] New post 11 May 2004, 12:24
Answer is A
at least two sides of the quadrilateral will be equal.
A is enough.
B is not enough
Hence the answer is A
_________________

Best wishes
Chetan

Senior Manager
Senior Manager
avatar
Joined: 26 Jan 2004
Posts: 402
Location: India
Followers: 1

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

 [#permalink] New post 12 May 2004, 00:04
Emmanuel: I still didn't get your logic
Why this is so? If you mark points, where circle inscribed touches quadr. by A1, B1, C1, D1, then |AA1| = |AD1|, |BA1| = |BB1|, |CB1| = |CC1|, |DC1| = |DD1| => since AB = AA1 + BA1, BC = BB1 + CB1, CD = CC1 + DC1, DA = DD1 + AD1, AB + CD = BC + AD.

How come from above logic you can say (AB+CD=BC+AD)?
(Before joining this group I was under illusion that I am an expert in Maths!!! :roll: )
Manager
Manager
User avatar
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 9 [0], given: 0

mba!!!... [#permalink] New post 12 May 2004, 00:35
mba wrote:
Emmanuel: I still didn't get your logic
Why this is so? If you mark points, where circle inscribed touches quadr. by A1, B1, C1, D1, then |AA1| = |AD1|, |BA1| = |BB1|, |CB1| = |CC1|, |DC1| = |DD1| => since AB = AA1 + BA1, BC = BB1 + CB1, CD = CC1 + DC1, DA = DD1 + AD1, AB + CD = BC + AD.

How come from above logic you can say (AB+CD=BC+AD)?
(Before joining this group I was under illusion that I am an expert in Maths!!! :roll: )


OK, see this:
Attachments

4.GIF
4.GIF [ 8.99 KiB | Viewed 4109 times ]

Intern
Intern
avatar
Joined: 31 Mar 2004
Posts: 28
Location: texas
Followers: 1

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

 [#permalink] New post 12 May 2004, 00:49
nice job emmauel..thanks for making it more clear...
Senior Manager
Senior Manager
avatar
Joined: 26 Jan 2004
Posts: 402
Location: India
Followers: 1

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

 [#permalink] New post 12 May 2004, 23:31
Thanks, emmanuel.

(Now I wonder how come I didn't see this thing earlier, :beat )
SVP
SVP
User avatar
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 46 [0], given: 0

 [#permalink] New post 13 May 2004, 06:20
Wow! I really liked Emmanuel's solution.
  [#permalink] 13 May 2004, 06:20
Display posts from previous: Sort by

Given a quadrilateral ABCD, a circle is inscribed in the

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.