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

 It is currently 25 Sep 2018, 10:08

### 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 the length of the minor arc AB is 10pi and the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Dec 2014
Posts: 30
In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

Updated on: 24 Aug 2016, 04:08
8
00:00

Difficulty:

85% (hard)

Question Stats:

55% (02:57) correct 45% (03:01) wrong based on 84 sessions

### HideShow timer Statistics

In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle F, if the radius of the circle is 18?

(A) 20
(B) 25
(C) 30
(D) 35
(E) 40

Source: OptimusPrep

LE: Updated. Had some editing issues first time.

Attachments

circle.JPG [ 14.42 KiB | Viewed 2155 times ]

Originally posted by Stn on 24 Aug 2016, 02:45.
Last edited by Stn on 24 Aug 2016, 04:08, edited 1 time in total.
 Optimus Prep Discount Codes Kaplan GMAT Prep Discount Codes Magoosh Discount Codes
Retired Moderator
Joined: 26 Nov 2012
Posts: 595
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

24 Aug 2016, 03:51
Please share the options and there is no E but I see F..
Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 233
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

24 Aug 2016, 03:57
Stn wrote:
In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle E, if the radius of the circle is 18?

Source: OptimusPrep

Is it 70 degree?

Angle of Major Arc - Angle of Minor Arc = 100 - 30 = 70 Degree. (Not Sure about this).

Cheers
Balaji
_________________

Aiming for a 3 digit number with 7 as hundredths Digit

Intern
Joined: 02 Feb 2016
Posts: 2
In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

24 Aug 2016, 07:43
1
1
The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can
calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees.
(Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees.
Now In TRIANGLE CBF,
angle B(CBD) =15
angle C(BCF) =130
thus angle F= 180 - (B + C)
= 180 - 145
= 35

(D)
Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 233
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

24 Aug 2016, 07:56
Well explained Shashank. Missed to divide by 2

Cheers
Balaji
_________________

Aiming for a 3 digit number with 7 as hundredths Digit

Intern
Joined: 10 Mar 2015
Posts: 41
Location: India
GMAT 1: 700 Q49 V37
GPA: 3.9
WE: Web Development (Computer Software)
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

24 Aug 2016, 08:04
My Approach:

CB is diameter, A is a point on the semi circle..so Angle A will be 90 degrees.
Given radius = 18. So the length of the arc BAC is 18pi.
Given AB = 10pi So AC = 8pi

AC = 8pi, CD = 3pi, So AD = 11pi.
At centre, AD subtends and angle 110 degrees.( By comparing 18pi spans 180 degrees)
So at B, AD subtends an angle of 110/2 = 55 degrees

90 degrees + 55 degrees + Angle at F = 180 degrees.
Therefore F = 35 degrees
Intern
Joined: 22 Feb 2017
Posts: 15
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

28 Apr 2017, 02:59
Stn wrote:
In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle F, if the radius of the circle is 18?

(A) 20
(B) 25
(C) 30
(D) 35
(E) 40

Source: OptimusPrep

LE: Updated. Had some editing issues first time.

CB or CB is diameter how can you assume that its not given in the question stem?? and by any means with the help of info given in the question can you prove CB is the diameter??
Intern
Joined: 21 May 2016
Posts: 23
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

28 Apr 2017, 07:29
shashanksst94 wrote:
The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can
calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees.
(Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees.
Now In TRIANGLE CBF,
angle B(CBD) =15
angle C(BCF) =130
thus angle F= 180 - (B + C)
= 180 - 145
= 35

(D)

Can someone please explain how we arrived at angle C (BCF) = 130?
Manager
Joined: 26 Sep 2016
Posts: 62
Re: In the circle above the length of the minor arc AB is 10pi and the  [#permalink]

### Show Tags

02 Oct 2017, 02:06
shashanksst94 wrote:
The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can
calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees.
(Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees.
Now In TRIANGLE CBF,
angle B(CBD) =15
angle C(BCF) =130
thus angle F= 180 - (B + C)
= 180 - 145
= 35

(D)

Hi ,
But what if BC is not the diameter of the circle? It is not given in the question. Can we solve the question the same way without this info?
Re: In the circle above the length of the minor arc AB is 10pi and the &nbs [#permalink] 02 Oct 2017, 02:06
Display posts from previous: Sort by

# In the circle above the length of the minor arc AB is 10pi and the

## 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®.