NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 01:10 It is currently 24 Apr 2024, 01:10
Decision Tracker
My Rewards
New posts
New comers' posts

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

If A is the center of the circle shown above (see attachment

SORT BY:
Date
Kudos
Tags:
Difficulty: 605-655 Levelx   Geometryx            
Find Similar Topics 
Show Tags
Hide Tags
User avatar
TheRob
Manager
Manager
Joined: 29 May 2008
Posts: 88
Own Kudos [?]: 718 [92]
Given Kudos: 0
Send PM
If A is the center of the circle shown above (see attachment [#permalink] New post   Updated on: 18 Jul 2022, 08:11
6
Kudos
86
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

70% (02:05) correct 30% (02:08) wrong based on 1525 sessions
Hide Show timer Statistics

If A is the center of the circle shown above and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75

PS21278

Show Spoiler
Attachment:
Circle - original.PNG
Circle - original.PNG [ 3.31 KiB | Viewed 47804 times ]
Attachment:
21278-0.png
21278-0.png [ 32.38 KiB | Viewed 19443 times ]

ShowHide Answer
Official Answer
B

Originally posted by TheRob on 07 Sep 2009, 07:19.
Last edited by Bunuel on 18 Jul 2022, 08:11, edited 4 times in total.
Edited the question, added the diagram and added the OA
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92892
Own Kudos [?]: 618668 [27]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   22 May 2020, 07:15
2
Kudos
25
Bookmarks
Expert Reply

If A is the center of the circle shown above and AB = BC = CD, what is the value of x ?

A. 15
B. 30
C. 45
D. 60
E. 75


PS21278

Show Spoiler
Attachment:
1.png
1.png [ 7.92 KiB | Viewed 13620 times ]
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92892
Own Kudos [?]: 618668 [26]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   25 Feb 2012, 12:41
16
Kudos
9
Bookmarks
Expert Reply
TheRob wrote:

If A is the center of the circle shown above (see attachment) and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75
Attachment:
The attachment Circle - original.PNG is no longer available




Look at the diagram below:
Attachment:
Circle.PNG
Circle.PNG [ 26.39 KiB | Viewed 49500 times ]
Given that AB = BC = CD, also since AB is the radius then AB = AC = AD = radius, so we have that: AB = BC = CD = AC = AD, so basically we have two equilateral triangles ABC and ACD with common base of AC (ABC and ACD are mirror images of each other). Line segment BD cuts the angle ABC in half and since all angles in equilateral triangle equal to 60 degrees then x=60/2=30 degrees.

Answer: B.
General Discussion
User avatar
Jivana
Senior Manager
Senior Manager
Joined: 20 Mar 2008
Posts: 340
Own Kudos [?]: 393 [16]
Given Kudos: 5
Send PM
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   07 Sep 2009, 18:49
13
Kudos
3
Bookmarks
Triangle abc is equilateral, therefore all angles are 60. abc = acb = bac = 60.
Similarly, Triangle adc is equilateral, therefore all angles are 60. adc = acd = dac = 60.

Now, angle bad = bac + dac = 120, since each triangle is a reverse image of the other.

Now triangle bad is isosceles, since ab = ad.
Therefore abd = adb = 30, since bad =120.

Hence, B
User avatar
MBAhereIcome
Current Student
Joined: 07 Aug 2011
Status:mba here i come!
Posts: 151
Own Kudos [?]: 1938 [6]
Given Kudos: 48
Send PM
GMAT ToolKit User
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   25 Feb 2012, 11:55
5
Kudos
1
Bookmarks
you can solve the question easily by knowing two important properties of square and rhombus.

1. diagonals bisect each other.
2. each diagonal forms a 90 degree angle with the other diagonal
avatar
pbull78
Intern
Intern
Joined: 16 Dec 2011
Posts: 28
Own Kudos [?]: 19 [0]
Given Kudos: 12
GMAT Date: 04-23-2012
Send PM
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   27 Feb 2012, 08:25
bunuel ,

how can we say that line segment BD cuts the angle ABC in half which property is this , can u expalin me?
thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92892
Own Kudos [?]: 618668 [2]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   27 Feb 2012, 08:42
2
Kudos
Expert Reply
pbull78 wrote:
bunuel ,

how can we say that line segment BD cuts the angle ABC in half which property is this , can u expalin me?
thanks


ABC and ACD are two equilateral triangles, which are mirror images of each other if you join vertices B and D, the segment BD must cut AC, the common base, in half. Which makes BD perpendicular bisector of AC --> so BO is a hight, median, and bisector of angle ABC (O being intersection point of BD and AC).

Hope it's clear.
avatar
aakrity
Intern
Intern
Joined: 08 Oct 2011
Posts: 25
Own Kudos [?]: 83 [0]
Given Kudos: 38
Send PM
GMAT ToolKit User
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   14 Nov 2013, 02:44
we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD

This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45

Why is this not considered that ABCD is a square?
Attachments

Circle.PNG
Circle.PNG [ 26.39 KiB | Viewed 42793 times ]

User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92892
Own Kudos [?]: 618668 [1]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   14 Nov 2013, 02:49
1
Kudos
Expert Reply
aakrity wrote:
we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD

This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45

Why is this not considered that ABCD is a square?


ABCD is not a square it's a rhombus (the diagonals are not equal).
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13376 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   16 Feb 2020, 23:09
Expert Reply
TheRob wrote:
Attachment:
Circle - original.PNG
If A is the center of the circle shown above and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75


Adding teh video solution to teh thread.

avatar
B
Batman117
Intern
Intern
Joined: 19 Jan 2019
Posts: 45
Own Kudos [?]: 13 [2]
Given Kudos: 276
Location: India
Concentration: Operations, Strategy
GPA: 3.3
Send PM
Reviews Badge
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   22 May 2020, 07:47
2
Kudos
Here AB=BC
Where AB is radius.
From figure AC is also radius.
So AB=BC=AC
So ABC is equilateral triangle.
So each side is of 60
So X=60/2
X=30

Posted from my mobile device
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29900 [5]
Given Kudos: 799
Location: Canada
Send PM
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   23 May 2020, 15:52
4
Kudos
1
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:

If A is the center of the circle shown above and AB = BC = CD, what is the value of x ?

A. 15
B. 30
C. 45
D. 60
E. 75
PS21278
Show Spoiler
Attachment:
1.png


Since all of the radii in a circle have the same length, we know that the 3 red lines below all have the same length.



Since we are told that AB = BC = CD, we can say that all 5 red lines below have the same length



This means the two red triangles must be equilateral triangles, which means all of their angles are 60°



Since all 4 sides of the red quadrilateral below have the same length, we know that the quadrilateral is a rhombus


In a rhombus, the diagonals bisect the angles.
So the blue diagonal above, bisects the 60° angle into two equal angles of 30° each, which means x = 30

Answer: B

Cheers,
Brent
User avatar
B
Rainman91
Manager
Manager
Joined: 03 Jul 2020
Posts: 89
Own Kudos [?]: 24 [0]
Given Kudos: 120
Send PM
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   31 Jul 2022, 04:05
Do we assume that the lines are touching the circle's circumference? Just based on the image?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32639
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If A is the center of the circle shown above (see attachment [#permalink] New post   11 Jan 2024, 10:09
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
gmatclubot
Re: If A is the center of the circle shown above (see attachment [#permalink]
11 Jan 2024, 10:09
Moderators:
Bunuel
Math Expert
92888 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions