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

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Math Expert
Joined: 02 Sep 2009
Posts: 56306
In the circle above, centered on point O, angle AOB measures 40 degree  [#permalink]

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04 Apr 2018, 23:21
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Difficulty:

35% (medium)

Question Stats:

79% (01:30) correct 21% (01:15) wrong based on 46 sessions

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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:

ArcBC.png [ 7.73 KiB | Viewed 942 times ]

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

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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

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

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

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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 708 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

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

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Re: In the circle above, centered on point O, angle AOB measures 40 degree  [#permalink]

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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

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.

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