Last visit was: 25 Apr 2026, 02:27 It is currently 25 Apr 2026, 02:27
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,130
 [16]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,130
 [16]
What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Jul 2016, 04:00
1
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

33% (01:30) correct 67% (01:49) wrong based on 186 sessions

History

Date
Time
Result
Not Attempted Yet

What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Show Spoiler
Attachment:
untitled.JPG
untitled.JPG [ 5.22 KiB | Viewed 4605 times ]
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 25 Apr 2026
Posts: 6,977
Own Kudos:
16,915
 [7]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,977
Kudos: 16,915
 [7]
What is the perimeter of quadrangle ABCD in which a circle is inscribe 03 Nov 2016, 22:39
5
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel

What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Show Spoiler
Attachment:
The attachment untitled.JPG is no longer available
Show more

Please check the detailed explanation in the attached picture

Answer: Option A
Attachments

File comment: www.GMATinsight.com
121.jpg
121.jpg [ 117.87 KiB | Viewed 3946 times ]

General Discussion
avatar
kshitij ghildiyal
avatar
Joined: 29 Jul 2015
Last visit: 18 May 2020
Posts: 26
Own Kudos:
26
 [3]
Given Kudos: 9
Location: India
Concentration: Other
Schools: ISB '18 (A$) Goizueta '19 (S) Krannert '19 (WD) Kenan-Flagler '19 (D) Arizona State"19 (WD)
GMAT 1: 720 Q50 V38
GPA: 2.9
Schools: ISB '18 (A$) Goizueta '19 (S) Krannert '19 (WD) Kenan-Flagler '19 (D) Arizona State"19 (WD)
GMAT 1: 720 Q50 V38
Posts: 26
Kudos: 26
 [3]
What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Jul 2016, 09:29
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
there can be only two tangents to a circle from any exterior pt. and they are of equal length.. (i.e. from pt. of origin to pt. of contact...
SO the perimeter of the quadilateral will be effectively 2 ( AB + DC )...

so il go with A..
User avatar
law258
User avatar
Joined: 05 Sep 2016
Last visit: 11 Oct 2020
Posts: 259
Own Kudos:
121
Given Kudos: 283
Status:DONE!
Posts: 259
Kudos: 121
What is the perimeter of quadrangle ABCD in which a circle is inscribe 02 Nov 2016, 15:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone please explain this? I don't understand the underlying concept.

Thanks in advance! :)
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,384
Own Kudos:
5,236
Given Kudos: 1,228
Location: India
Products:
My Reviews
Posts: 1,384
Kudos: 5,236
What is the perimeter of quadrangle ABCD in which a circle is inscribe 03 Nov 2016, 07:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lawiniecke
Can someone please explain this? I don't understand the underlying concept.

Thanks in advance! :)
Show more

Refer the attached figure.

Draw a line from center O to corner C. Now, consider triangles ROC and QOC. Since OR = OQ and hypotenuse OC is common between the two triangles RC = QC = l.

Repeat the same procedure and we find out that perimeter of quadrangle ABCD = 2k + 2l + 2m + 2n = 2(k + n + m + l) = 2(AB + CD).

So statement 1 by itself is sufficient.

St2 --> m + l = 5. Clearly insufficient as we do not know the value of k + n.

Answer: A
Attachments

IMG_20161103_200853.jpg
IMG_20161103_200853.jpg [ 1.01 MiB | Viewed 4024 times ]

avatar
omkar8275
avatar
Joined: 01 Aug 2019
Last visit: 11 Feb 2021
Posts: 6
Given Kudos: 111
Posts: 6
Kudos: 0
What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Nov 2019, 18:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Show Spoiler
Attachment:
untitled.JPG
Show more

If you want to understand the underlying concept in this problem, search for the Pitot theorem.

According to the Pitot theorem, the sum of pairs of opposite sides is the same.

Therefore, AB+CD= BC+AD.
Statement 1 is sufficient to answer the question. Statement 2 does not answer the question on its own.
Hence, Answer choice A is correct.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,977
Own Kudos:
1,117
Posts: 38,977
Kudos: 1,117
What is the perimeter of quadrangle ABCD in which a circle is inscribe 06 Feb 2020, 21:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109822 posts
kingbucky
498 posts
Gmat860sanskar
212 posts