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

 It is currently 18 Oct 2019, 12:14

### 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 with center O, what is the length of minor arc BC?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
In the circle above with center O, what is the length of minor arc BC?  [#permalink]

### Show Tags

15 Jan 2018, 21:53
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:06) correct 24% (01:18) wrong based on 71 sessions

### HideShow timer Statistics

In the circle above with center O, what is the length of minor arc BC?

(1) Diameter AC = 24
(2) Chord AB = $$12\sqrt{3}$$

Attachment:

BAC_Circle_O.png [ 11.81 KiB | Viewed 2467 times ]

_________________
Senior Manager
Joined: 17 Oct 2016
Posts: 313
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: In the circle above with center O, what is the length of minor arc BC?  [#permalink]

### Show Tags

15 Jan 2018, 22:10
D

From the figure we can understand that this is 30-60-90 right traingle and the sides AC:AB:BC=2:sqrt(3):1. We need the value of radius (OC) and the angle BOC to find the arc length.

from st1 we get AC=24. Hence OC=12 and BC=12 from the ratio. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.
from st2 we get AB=12.sqrt(3). Hence from the ratio we get BC=12 and AC=24, OC =12. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.

Posted from my mobile device
_________________
Help with kudos if u found the post useful. Thanks
Director
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: In the circle above with center O, what is the length of minor arc BC?  [#permalink]

### Show Tags

15 Jan 2018, 22:14
Bunuel wrote:

In the circle above with center O, what is the length of minor arc BC?

(1) Diameter AC = 24
(2) Chord AB = $$12\sqrt{3}$$

Attachment:
BAC_Circle_O.png

Area of minor arc = 2(Pi)r(center angle/360)

(1) Diameter AC = 24

Angle at the center is twice the Angle at circumference

Center angle = 60

And Also r=12

Hence Suff

(2) Chord AB = $$12\sqrt{3}$$

Join BC & it is 30-60-90

We can find the Diameter & radius

Hence suff

Hence D
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Intern
Joined: 03 Jun 2015
Posts: 21
GMAT 1: 710 Q49 V44
GPA: 3.58
WE: Information Technology (Computer Software)
Re: In the circle above with center O, what is the length of minor arc BC?  [#permalink]

### Show Tags

15 Jan 2018, 22:40
Property used : Any angle cast on circumference of circle which has diameter as base is a 90 degree angle.

[Given] : Value of one angle of triangle ABC i.e 30 degree

[Required] : Length of BC

Solution : Since we have a right triangle ABC, all we need is to apply basic trigonometry to find length of BC.

Both options suggest length of chord. Any one of the option value can be used to find the length of BC.

Hence , option D is the right answer.
_________________
A dream doesn't become reality through magic; it takes sweat, determination and hard work.
Re: In the circle above with center O, what is the length of minor arc BC?   [#permalink] 15 Jan 2018, 22:40
Display posts from previous: Sort by