GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2019, 02:59

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.

Close

Request Expert Reply

Confirm Cancel

Which of the figures below can be inscribed in a circle?

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 31 Oct 2011
Posts: 213
Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 21 Feb 2012, 03:04
2
25
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

52% (00:57) correct 48% (00:59) wrong based on 363 sessions

HideShow timer Statistics

Which of the figures below can be inscribed in a circle?
Image
(A) I only

(B) III only
(C) I & III only
(D) II & III only
(E) I, II & III

Attachment:
IMG_0414.jpg
IMG_0414.jpg [ 2.46 MiB | Viewed 7003 times ]
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59087
Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 21 Feb 2012, 04:10
7
13
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

Image

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°). See Central Angle Theorem in Circles chapter of Math Book: http://gmatclub.com/forum/math-circles-87957.html.

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59087
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 20 Jun 2013, 06:39
Intern
Intern
avatar
Joined: 15 Jun 2013
Posts: 5
Concentration: Strategy, Finance
GMAT Date: 02-13-2014
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 24 Sep 2013, 02:10
1
Bunuel wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°).

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.


I agree with "the opposite angles are supplementary" concept and I did the same.
Can this be a solution @Bunuel ?
1. for first diagram - Moreover, isn't the first one isoceles trapezium ? Isn't that sufficient ?
2. for third diagram - Parallelogram inscribed in a circle will become a rectangle (think of shape shifting)
Intern
Intern
avatar
Joined: 01 Jan 2015
Posts: 17
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 20 Jun 2015, 03:26
Bunuel wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°). See Central Angle Theorem in Circles chapter of Math Book: math-circles-87957.html.

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.


Hi Bunuel,
By 'opposite angles' you mean diagonally opposite angles right? otherwise even II can be inscribed in a circle.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 20 Jun 2015, 03:39
NavenRk wrote:
Bunuel wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°). See Central Angle Theorem in Circles chapter of Math Book: math-circles-87957.html.

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.


Hi Bunuel,
By 'opposite angles' you mean diagonally opposite angles right? otherwise even II can be inscribed in a circle.


Yes Diagonally opposite angles should sum up to 180 degree for the quadrilateral to be inscribed in a circle.

This property is a derived property from the one which says that angle subtended by any segment at the centre of the circle should be twice the angle subtended by the same segment on the circumference of the same circle.

Such Quadrilaterals which can be inscribed in a circle are called "Cyclic Quadrilateral"
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Manager
avatar
B
Joined: 23 Oct 2017
Posts: 60
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 10 Jan 2018, 19:12
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?
Image
(A) I only
(B) III only
(C) I & III only
(D) II & III only
(E) I, II & III

Attachment:
IMG_0414.jpg


------------------
If a quadrilateral can be inscribed in a circle then the sum of its opposite angles =180
only 2 of the quadrilaterals meet this criteria
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13596
Re: Which of the figures below can be inscribed in a circle?  [#permalink]

Show Tags

New post 25 Mar 2019, 17:59
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 Club Bot
Re: Which of the figures below can be inscribed in a circle?   [#permalink] 25 Mar 2019, 17:59
Display posts from previous: Sort by

Which of the figures below can be inscribed in a circle?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne