Last visit was: 25 Apr 2026, 16:27 It is currently 25 Apr 2026, 16:27
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
 1   2   
705-805 (Hard)|   Geometry|      
User avatar
PathFinder007
User avatar
Joined: 10 Mar 2014
Last visit: 21 Oct 2018
Posts: 127
Own Kudos:
745
 [142]
Given Kudos: 13
Posts: 127
Kudos: 745
 [142]
In the figure AB and CD are two diameters of circle. Interse Updated on: 04 Dec 2014, 04:32
Originally posted by PathFinder007 on 03 Aug 2014, 02:28.
Last edited by Bunuel on 04 Dec 2014, 04:32, edited 1 time in total.
Edited the question.
8
Kudos
Add Kudos
132
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:

75% (hard)

Question Stats:

59% (02:38) correct 41% (02:44) wrong based on 1175 sessions

History

Date
Time
Result
Not Attempted Yet
Attachment:
Circle_Angle.JPG
Circle_Angle.JPG [ 16.89 KiB | Viewed 30711 times ]
In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A. 114
B. 100
C. 80
D. 96
E. 40
ShowHide Answer
Official Answer
A
Every tricky question should trigger a follow up quiz. Build that habit with GMAT Club Forum Quiz →.
Most Helpful Reply
User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
822
 [30]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 822
 [30]
In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:39
20
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
Show more

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Attachments

circle.png
circle.png [ 41.27 KiB | Viewed 30030 times ]

User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
822
 [17]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 822
 [17]
In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 02:37
13
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,465
 [12]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,465
 [12]
In the figure AB and CD are two diameters of circle. Interse 12 Nov 2018, 09:17
11
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
PathFinder007
Attachment:
Circle_Angle.JPG
In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A. 114
B. 100
C. 80
D. 96
E. 40
Show more

Let's use some useful circle properties

First let's add a blue line, to divide ∠CEB into 2 angles



CD is the DIAMETER of the circle
Since ∠CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that ∠CED = 90°



Now recognize that the intersection of AB and CD creates two equal (vertically opposite) angles, we can conclude the angle opposite the 48° is also 48°



Now recognize that we have two angles containing (aka "holding") the arc BD
Property: If a CENTRAL angle and an INSCRIBED angle contain the same arc, then the CENTRAL angle is TWICE the INSCRIBED angle
This means that ∠DEB = 24°


At this point, we have:

So, ∠CEB = 90° + 24° = 114°

Answer: A

RELATED VIDEO FROM OUR COURSE
General Discussion
User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
822
 [1]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 822
 [1]
In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 02:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PathFinder007
In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A 114
B 100
C 80
D 96
E 40
Show more


Kudos from me, because I love problems with central angles:)
User avatar
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 188
Own Kudos:
469
 [1]
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 188
Kudos: 469
 [1]
In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 03:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.
Show more


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
avatar
saikrishna123
avatar
Joined: 31 Jul 2014
Last visit: 10 Feb 2015
Posts: 17
Own Kudos:
12
Given Kudos: 12
Posts: 17
Kudos: 12
In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 19:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
Show more

According to me, CB is not the diameter. So central angle doesnt apply in this case. Also, COB is 138 and not 228.
avatar
venkat18290
avatar
Joined: 01 Apr 2013
Last visit: 05 May 2017
Posts: 11
Own Kudos:
12
 [8]
Given Kudos: 37
Schools: Tepper '16 (S)
Schools: Tepper '16 (S)
Posts: 11
Kudos: 12
 [8]
In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:02
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
Show more

Hi buddy,

COB is indeed 180-48 = 132 degrees . There is a concept of major and minor segment ( please google this ) Now the point O is in the minor segment of the arc and in this case it would be half of the angle subtended in the major segment i.e ( 360-132) = 228 /2 = 114 .
User avatar
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 188
Own Kudos:
469
 [1]
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 188
Kudos: 469
 [1]
In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
smyarga
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Show more


Now I got the explanation. Thanks for the help.
User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
822
 [3]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 822
 [3]
In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 13:31
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
desaichinmay22, specially for you another nice problem with central angle if-the-radius-of-the-circle-below-see-attachment-is-equal-175709.html
User avatar
saggii27
User avatar
Joined: 15 Jul 2012
Last visit: 31 Mar 2016
Posts: 23
Own Kudos:
62
Given Kudos: 245
Posts: 23
Kudos: 62
In the figure AB and CD are two diameters of circle. Interse 05 Aug 2014, 06:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
smyarga
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Show more

Hi Smyarga,
how did you get 180 degrees?
i thought about vertically opposite angles then realised that i was wrong.
User avatar
smyarga
User avatar
Tutor
Joined: 20 Apr 2012
Last visit: 06 Aug 2020
Posts: 82
Own Kudos:
822
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Expert
Expert reply
GMAT 2: 730 Q51 V38
Posts: 82
Kudos: 822
In the figure AB and CD are two diameters of circle. Interse 05 Aug 2014, 07:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
saggii27
smyarga
desaichinmay22



Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.


Hi Smyarga,
how did you get 180 degrees?
i thought about vertically opposite angles then realised that i was wrong.
Show more


Since COD is straight.
User avatar
farhanchaudhary
User avatar
Current Student
Joined: 14 Jul 2013
Last visit: 24 Mar 2026
Posts: 272
Own Kudos:
433
 [5]
Given Kudos: 131
Products:
My Reviews
Posts: 272
Kudos: 433
 [5]
In the figure AB and CD are two diameters of circle. Interse 06 Aug 2014, 04:25
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
PathFinder007
In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A 114
B 100
C 80
D 96
E 40
Show more


Join Segment AE in the figure, we know Angle AEC is half of Angle COA(Assuming diameter intersect at point O).

Angle AEC = 24
Ab is diameter, so Angle AEB = 90
Angle CEB = 90+24 = 114
User avatar
maggie27
User avatar
Joined: 25 Apr 2014
Last visit: 19 May 2015
Posts: 75
Own Kudos:
368
Given Kudos: 1,474
Posts: 75
Kudos: 368
In the figure AB and CD are two diameters of circle. Interse 28 Aug 2014, 20:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi there,
Can someone explain me this with the help of proper diagram,unable to get it!
User avatar
arnabs
User avatar
Joined: 06 Aug 2013
Last visit: 29 Oct 2020
Posts: 44
Own Kudos:
16
 [4]
Given Kudos: 17
Posts: 44
Kudos: 16
 [4]
In the figure AB and CD are two diameters of circle. Interse 04 Dec 2014, 00:07
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
smyarga
desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Show more


another approach,

join C and A. since AB is the diameter, A, C, E and B form a cyclic quadrilateral. now opposit angles of cyclic quadrilaterals sum up to 180 degrees. considering the point of intersection of the 2 diameters as O.

angle AOC = 48 degrees. ........... given
OA = OC, radius of the circle, hence trianlge OAC is isoceles.
thus angle ACO = angle OAC = 66 degrees.

now,
angle OAC + angle CEB = 180 degrees......... since opposit angles of cyclic quadrilaterals sum up to 180 degrees.
therefore, angle CEB = 180 - 66 = 114 degrees.

hope this was helpful.

kudos if you like. :)
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,681
 [2]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,681
 [2]
In the figure AB and CD are two diameters of circle. Interse Updated on: 27 Nov 2021, 09:01
Originally posted by BrushMyQuant on 14 Dec 2014, 21:42.
Last edited by BrushMyQuant on 27 Nov 2021, 09:01, edited 1 time in total.
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please tag this to PS instead of DS
Thank you!

Watch the following video to Learn Basics of Circles

User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,830
Own Kudos:
811,281
Given Kudos: 105,886
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: 109,830
Kudos: 811,281
In the figure AB and CD are two diameters of circle. Interse 15 Dec 2014, 08:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nktdotgupta
Please tag this to PS instead of DS
Thank you!
Show more

Moved to PS forum. Thank you for noticing this.
User avatar
Shree9975
User avatar
Joined: 06 Mar 2014
Last visit: 16 Feb 2016
Posts: 61
Own Kudos:
61
Given Kudos: 3
Posts: 61
Kudos: 61
In the figure AB and CD are two diameters of circle. Interse 18 Dec 2014, 04:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
 [1]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
 [1]
In the figure AB and CD are two diameters of circle. Interse 18 Dec 2014, 05:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shree9975
Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?
Show more

Angle COB is not 180.

Note that the angle around O will be 360 degrees. There is angle COB, the smaller angle (the angle that arc CEB subtends at the center) and angle COB, the larger angle (shown by red arrow around center O in the second diagram). The major arc CADB subtends larger angle COB at the center and inscribed angle CEB at the circle. The central angle will be twice the inscribed angle.

The larger angle COB = angle COA + angle AOD + angle DOB = 180 + 48 = 228 = Central angle

Inscribed angle = 228/2 = 114

Answer (A)
avatar
Radhika11
avatar
Joined: 25 May 2014
Last visit: 20 Jul 2016
Posts: 23
Own Kudos:
148
Given Kudos: 59
Posts: 23
Kudos: 148
In the figure AB and CD are two diameters of circle. Interse 24 Oct 2015, 06:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
Shree9975
Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?

Angle COB is not 180.

Note that the angle around O will be 360 degrees. There is angle COB, the smaller angle (the angle that arc CEB subtends at the center) and angle COB, the larger angle (shown by red arrow around center O in the second diagram). The major arc CADB subtends larger angle COB at the center and inscribed angle CEB at the circle. The central angle will be twice the inscribed angle.

The larger angle COB = angle COA + angle AOD + angle DOB = 180 + 48 = 228 = Central angle

Inscribed angle = 228/2 = 114

Answer (A)
Show more


Hi Karishma

can't we take this way that smaller COB is 132 and then CEB = 180 - (132/2) ? using cyclic quadrilateral property.
 1   2   
Moderators:
Bunuel
Math Expert
109830 posts
Krunaal
Tuck School Moderator
852 posts