GMAT Changed on April 16th - Read about the latest changes here

 It is currently 21 Apr 2018, 19:40

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the circle above, centered on point O, angle AOB measures 40 degree

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44599
In the circle above, centered on point O, angle AOB measures 40 degree [#permalink]

### Show Tags

04 Apr 2018, 23:21
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

88% (01:07) correct 13% (00:57) wrong based on 24 sessions

### HideShow timer Statistics

In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 7π

[Reveal] Spoiler:
Attachment:

ArcBC.png [ 7.73 KiB | Viewed 329 times ]
[Reveal] Spoiler: OA

_________________
Intern
Joined: 03 Aug 2016
Posts: 34
In the circle above, centered on point O, angle AOB measures 40 degree [#permalink]

### Show Tags

04 Apr 2018, 23:47
Bunuel wrote:

In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 7π

[Reveal] Spoiler:
Attachment:
ArcBC.png

Given: AOB = 40 degrees; BD = 18 inches

BD is the diameter --> radius = 18/2 = 9 inches.

AOB = 40 degrees, then, BOC (which is holding the minor arc BC in question) = 140 degrees.

Length of the minor arc = (n/360) (2*π*r) --> (140/360) (2*π*9) = 7π

_________________

SC Moderator
Joined: 22 May 2016
Posts: 1546
In the circle above, centered on point O, angle AOB measures 40 degree [#permalink]

### Show Tags

05 Apr 2018, 06:48
Bunuel wrote:
In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 7π

Attachment:

ArcBCed.png [ 11.24 KiB | Viewed 187 times ]

• Find arc BC's length as a fraction of circumference.

Arc BC's central angle measure
as a part of the circle's 360 degrees =
Arc BC's fraction of circumference

• Arc BC's central angle = ?
Arc BC's central angle lies on a straight line with
arc AB's central angle = 40°
So Arc BC's central angle = (180 - 40) = 140°

• Arc BC is what fraction of the circle's circumference?

$$\frac{Part}{Whole}=\frac{140°}{360°}=\frac{14}{36}=\frac{7}{18}$$

• Circumference of circle in inches?
BD = diameter = 18 inches
Circumference = $$\pi d = 18\pi$$ in

• Measure, in inches, of arc BC?
Arc BC $$=\frac{7}{18}$$ of circumference

$$\frac{7}{18}* 18\pi= 7\pi$$

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273
Re: In the circle above, centered on point O, angle AOB measures 40 degree [#permalink]

### Show Tags

10 Apr 2018, 11:02
Bunuel wrote:

In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 7π

[Reveal] Spoiler:
Attachment:
ArcBC.png

Since angle AOB is 40 degrees, angle BOC is 140 degrees.

Thus, arc BC is 140/360 = 14/36 = 7/18 of the entire circumference of the circle.

Since the diameter is 18, the circumference is 18π.

Thus, arc BC is 18π x 7/18 = 7π.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: In the circle above, centered on point O, angle AOB measures 40 degree   [#permalink] 10 Apr 2018, 11:02
Display posts from previous: Sort by