Last visit was: 24 Apr 2026, 23:01 It is currently 24 Apr 2026, 23:01
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
605-655 (Medium)|   Geometry|      
avatar
fozzzy
avatar
Joined: 29 Nov 2012
Last visit: 17 May 2015
Posts: 573
Own Kudos:
7,004
 [15]
Given Kudos: 543
Posts: 573
Kudos: 7,004
 [15]
In the circle above, CD is parallel to diameter AB and AB Updated on: 11 Jul 2018, 11:21
Originally posted by fozzzy on 22 Dec 2012, 03:39.
Last edited by Bunuel on 11 Jul 2018, 11:21, edited 3 times in total.
2
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

71% (02:08) correct 29% (02:18) wrong based on 267 sessions

History

Date
Time
Result
Not Attempted Yet

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π

(B) 7π/3

(C) 2π/3

(D) 4π/3

(E) 8π/3

Show Spoiler
Attachment:
circle_ABCD.png
circle_ABCD.png [ 7.77 KiB | Viewed 17823 times ]
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,094
 [9]
Given Kudos: 105,873
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: 109,818
Kudos: 811,094
 [9]
In the circle above, CD is parallel to diameter AB and AB 22 Dec 2012, 04:36
3
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π
(B) 7π3
(C) 2π3
(D) 4π3
(E) 8π3

Since CD is parallel to diameter AB, then <BCD=<ABC=30.

Next, Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

Minor arc \(BD=\frac{60}{360}*circumference=\frac{8\pi}{3}\).

Answer: E.

Identical question from GMAT Prep: in-the-circle-above-pq-is-parallel-to-diameter-or-93977.html
General Discussion
avatar
fozzzy
avatar
Joined: 29 Nov 2012
Last visit: 17 May 2015
Posts: 573
Own Kudos:
7,004
Given Kudos: 543
Posts: 573
Kudos: 7,004
In the circle above, CD is parallel to diameter AB and AB 22 Dec 2012, 04:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Any other way to solve this problem? if you didn't know the central angle theorem.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,094
 [1]
Given Kudos: 105,873
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: 109,818
Kudos: 811,094
 [1]
In the circle above, CD is parallel to diameter AB and AB 22 Dec 2012, 04:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fozzzy
Any other way to solve this problem? if you didn't know the central angle theorem.
Show more

Central Angle Theorem is a must know for GMAT. Check more here: math-circles-87957.html
avatar
fozzzy
avatar
Joined: 29 Nov 2012
Last visit: 17 May 2015
Posts: 573
Own Kudos:
7,004
 [1]
Given Kudos: 543
Posts: 573
Kudos: 7,004
 [1]
In the circle above, CD is parallel to diameter AB and AB 22 Dec 2012, 07:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
fozzzy
Any other way to solve this problem? if you didn't know the central angle theorem.

Central Angle Theorem is a must know for GMAT. Check more here: math-circles-87957.html
Show more

So I made changes to the diagram based on what I understood so <1 = 60, <2=30. Correct me If i'm wrong.
Attachments

circle_new.png
circle_new.png [ 15.6 KiB | Viewed 14901 times ]

User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,094
Given Kudos: 105,873
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: 109,818
Kudos: 811,094
In the circle above, CD is parallel to diameter AB and AB 23 Dec 2012, 06:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fozzzy
Bunuel
fozzzy
Any other way to solve this problem? if you didn't know the central angle theorem.

Central Angle Theorem is a must know for GMAT. Check more here: math-circles-87957.html

So I made changes to the diagram based on what I understood so <1 = 60, <2=30. Correct me If i'm wrong.
Show more

It's correct.

Check here: math-circles-87957.html
avatar
fozzzy
avatar
Joined: 29 Nov 2012
Last visit: 17 May 2015
Posts: 573
Own Kudos:
7,004
 [1]
Given Kudos: 543
Posts: 573
Kudos: 7,004
 [1]
In the circle above, CD is parallel to diameter AB and AB 25 Sep 2013, 01:19
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
I've added a modified image hope it helps and O is the center.

the portion in red is the arc with the respective angles

Angle COA = Angle DOB = 60 degrees

So the sum of the angles needs to be 180 degree so angle COD is 60 degree

after that apply the formula 2 pi R * 60 / 360 -----> we are given diameter 16 so then radius becomes 8

solve the equation we will get option E.
Attachments

Circle modified.png
Circle modified.png [ 8.44 KiB | Viewed 14324 times ]

User avatar
kanusha
User avatar
Joined: 25 Mar 2013
Last visit: 03 Aug 2017
Posts: 156
Own Kudos:
158
Given Kudos: 101
Location: United States
Concentration: Entrepreneurship, Marketing
Schools: Yale '17 HBS '17 Stanford '17
GPA: 3.5
Products:
My Reviews
Schools: Yale '17 HBS '17 Stanford '17
Posts: 156
Kudos: 158
In the circle above, CD is parallel to diameter AB and AB 25 Sep 2013, 22:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Central angle/360 = arc/circumference
So An inscribed angle is exactly half the corresponding central angle.
Inscribed angle is 30, then central angle is 60 so E….
Circumfrence = 2pir , so r= d/2, then 16pi
So 8pi/3, E….
User avatar
HMC
User avatar
Joined: 21 Jun 2016
Last visit: 06 Dec 2019
Posts: 56
Own Kudos:
29
Given Kudos: 9
Location: India
Posts: 56
Kudos: 29
In the circle above, CD is parallel to diameter AB and AB 06 Aug 2016, 00:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Learning for me : central angle is double the inscribed angle....

Sent from my Lenovo A7000-a using GMAT Club Forum mobile app
avatar
michaelkalend
avatar
Joined: 21 Mar 2017
Last visit: 29 May 2017
Posts: 15
Own Kudos:
29
Given Kudos: 6
Posts: 15
Kudos: 29
In the circle above, CD is parallel to diameter AB and AB 25 May 2017, 02:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π
(B) 7π3
(C) 2π3
(D) 4π3
(E) 8π3

Since CD is parallel to diameter AB, then <BCD=<ABC=30.

Next, Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

Minor arc \(BD=\frac{60}{360}*circumference=\frac{8\pi}{3}\).

Answer: E.

Identical question from GMAT Prep: https://gmatclub.com/forum/in-the-circle ... 93977.html
Show more

Hi Bunuel!

Would you be so kind and explain this point in more details please?
Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

As I understand, the central angle has to be twice more than other inscribed angle. Please clarify. This point.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,094
Given Kudos: 105,873
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: 109,818
Kudos: 811,094
In the circle above, CD is parallel to diameter AB and AB 25 May 2017, 02:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
michaelkalend
Bunuel

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π
(B) 7π3
(C) 2π3
(D) 4π3
(E) 8π3

Since CD is parallel to diameter AB, then <BCD=<ABC=30.

Next, Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

Minor arc \(BD=\frac{60}{360}*circumference=\frac{8\pi}{3}\).

Answer: E.

Identical question from GMAT Prep: https://gmatclub.com/forum/in-the-circle ... 93977.html

Hi Bunuel!

Would you be so kind and explain this point in more details please?
Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

As I understand, the central angle has to be twice more than other inscribed angle. Please clarify. This point.
Show more

Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle, so the central angle is twice the inscribed angle. You can check for more here: https://gmatclub.com/forum/math-circles-87957.html
avatar
michaelkalend
avatar
Joined: 21 Mar 2017
Last visit: 29 May 2017
Posts: 15
Own Kudos:
29
Given Kudos: 6
Posts: 15
Kudos: 29
In the circle above, CD is parallel to diameter AB and AB 25 May 2017, 03:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
michaelkalend
Bunuel

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π
(B) 7π3
(C) 2π3
(D) 4π3
(E) 8π3

Since CD is parallel to diameter AB, then <BCD=<ABC=30.

Next, Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

Minor arc \(BD=\frac{60}{360}*circumference=\frac{8\pi}{3}\).

Answer: E.

Identical question from GMAT Prep: https://gmatclub.com/forum/in-the-circle ... 93977.html

Hi Bunuel!

Would you be so kind and explain this point in more details please?
Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

As I understand, the central angle has to be twice more than other inscribed angle. Please clarify. This point.

Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle, so the central angle is twice the inscribed angle. You can check for more here: https://gmatclub.com/forum/math-circles-87957.html
Show more


Yes, that is absolutely clear! But how is that applied to the following:

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

How did you arrive with <BOD and does it mean that angle BOD is 120, while angle BCD is half which means it equals 60?
And if I am getting above correctly, how did you arrive that angle BOD is 120?

Please explain.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,094
 [2]
Given Kudos: 105,873
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: 109,818
Kudos: 811,094
 [2]
In the circle above, CD is parallel to diameter AB and AB 25 May 2017, 04:50
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
michaelkalend
Bunuel

In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π
(B) 7π3
(C) 2π3
(D) 4π3
(E) 8π3

Since CD is parallel to diameter AB, then <BCD=<ABC=30.

Next, Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

Minor arc \(BD=\frac{60}{360}*circumference=\frac{8\pi}{3}\).



Yes, that is absolutely clear! But how is that applied to the following:

Consider, O to be the center of the circle, then according to the central angle theorem above <BOD=2<BCD=60.

How did you arrive with <BOD and does it mean that angle BOD is 120, while angle BCD is half which means it equals 60?
And if I am getting above correctly, how did you arrive that angle BOD is 120?

Please explain.
Show more

Check the image below:


Blue (central angle) and Green (inscribed angle) subtend the same Red arc DB, thus (Blue angle) = 2*(Green angle).

H ope it's clear now.


Show Spoiler
Attachment:
Untitled.png
Untitled.png [ 14.66 KiB | Viewed 12288 times ]
User avatar
Leo8
User avatar
Joined: 23 May 2017
Last visit: 11 Sep 2020
Posts: 182
Own Kudos:
401
Given Kudos: 9
Concentration: Finance, Accounting
WE:Programming (Energy)
Posts: 182
Kudos: 401
In the circle above, CD is parallel to diameter AB and AB 25 May 2017, 11:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Attachment:
FullSizeRender (2).jpg
FullSizeRender (2).jpg [ 22.98 KiB | Viewed 10621 times ]

Length of the arc CDB = 2 pi * 4 * \(\frac{120}{360}\) =\(\frac{8 pi}{3}\)
User avatar
CounterSniper
User avatar
Joined: 20 Feb 2015
Last visit: 14 Apr 2023
Posts: 611
Own Kudos:
859
Given Kudos: 74
Concentration: Strategy, General Management
Posts: 611
Kudos: 859
In the circle above, CD is parallel to diameter AB and AB 11 Jul 2018, 11:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fozzzy
Attachment:
circle_ABCD.png
In the circle above, CD is parallel to diameter AB and AB has length 16. What is the length of arc DB?

(A) 2π

(B) 7π/3

(C) 2π/3

(D) 4π/3

(E) 8π/3
Show more

CD and AB are parallel .
Which means angle DCB and angle ABC are alternate angles
since alternate angles are equal
angle.DCB=angle.ABC=30
also ,
angle subtended by an arc at the centre of a circle = 2 * angle subtended by the same arc on any other point on the circle.

length of arc = 2pir@/360 (@= angle subtended by arc at the centre of the circle)
length of arc.BD=2*pi*8*60/360
8pi/3
E
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,978
Own Kudos:
1,117
Posts: 38,978
Kudos: 1,117
In the circle above, CD is parallel to diameter AB and AB 27 Feb 2023, 03:04
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
109818 posts
Krunaal
Tuck School Moderator
853 posts