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

 It is currently 16 Jul 2018, 01:58

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

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

In the circle above, CD is parallel to diameter AB and AB

Author Message
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 818
In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

Updated on: 11 Jul 2018, 11:21
1
10
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:29) correct 34% (01:33) wrong based on 254 sessions

HideShow timer Statistics

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

Attachment:

circle_ABCD.png [ 7.77 KiB | Viewed 9246 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

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.
Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

22 Dec 2012, 04:36
2
3

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 $$BD=\frac{60}{360}*circumference=\frac{8\pi}{3}$$.

Identical question from GMAT Prep: in-the-circle-above-pq-is-parallel-to-diameter-or-93977.html
_________________
General Discussion
Director
Joined: 29 Nov 2012
Posts: 818
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

22 Dec 2012, 04:54
Any other way to solve this problem? if you didn't know the central angle theorem.
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

22 Dec 2012, 04:57
1
fozzzy wrote:
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
_________________
Director
Joined: 29 Nov 2012
Posts: 818
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

22 Dec 2012, 07:27
1
Bunuel wrote:
fozzzy wrote:
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.
Attachments

circle_new.png [ 15.6 KiB | Viewed 7722 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

23 Dec 2012, 06:54
fozzzy wrote:
Bunuel wrote:
fozzzy wrote:
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.

It's correct.

Check here: math-circles-87957.html
_________________
Director
Joined: 29 Nov 2012
Posts: 818
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 Sep 2013, 01:19
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 [ 8.44 KiB | Viewed 7172 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Senior Manager
Joined: 25 Mar 2013
Posts: 265
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 Sep 2013, 22:30
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….
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Manager
Joined: 21 Jun 2016
Posts: 91
Location: India
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

06 Aug 2016, 00:03
Learning for me : central angle is double the inscribed angle....

Sent from my Lenovo A7000-a using GMAT Club Forum mobile app
Intern
Joined: 21 Mar 2017
Posts: 16
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 May 2017, 02:00
Bunuel wrote:

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 $$BD=\frac{60}{360}*circumference=\frac{8\pi}{3}$$.

Identical question from GMAT Prep: http://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.
Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 May 2017, 02:16
michaelkalend wrote:
Bunuel wrote:

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 $$BD=\frac{60}{360}*circumference=\frac{8\pi}{3}$$.

Identical question from GMAT Prep: http://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
_________________
Intern
Joined: 21 Mar 2017
Posts: 16
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 May 2017, 03:34
Bunuel wrote:
michaelkalend wrote:
Bunuel wrote:

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 $$BD=\frac{60}{360}*circumference=\frac{8\pi}{3}$$.

Identical question from GMAT Prep: http://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

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?

Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 May 2017, 04:50
michaelkalend wrote:
Bunuel wrote:

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?

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.

Attachment:

Untitled.png [ 14.66 KiB | Viewed 4404 times ]

_________________
Manager
Joined: 23 May 2017
Posts: 226
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

25 May 2017, 11:28
Attachment:

FullSizeRender (2).jpg [ 22.98 KiB | Viewed 3559 times ]

Length of the arc CDB = 2 pi * 4 * $$\frac{120}{360}$$ =$$\frac{8 pi}{3}$$
_________________

If you like the post, please award me Kudos!! It motivates me

Senior Manager
Joined: 20 Feb 2015
Posts: 421
Concentration: Strategy, General Management
Re: In the circle above, CD is parallel to diameter AB and AB [#permalink]

Show Tags

11 Jul 2018, 11:00
fozzzy wrote:
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

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
Re: In the circle above, CD is parallel to diameter AB and AB   [#permalink] 11 Jul 2018, 11:00
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.