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Points A, B, and C lie on a circle whose radius is 10 inches. If O is

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TBT
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Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   Updated on: 20 Mar 2023, 01:13
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Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(\frac{10 \pi }{ 3 }\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees
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D

Originally posted by TBT on 20 Mar 2023, 00:15.
Last edited by gmatophobia on 20 Mar 2023, 01:13, edited 1 time in total.
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   20 Mar 2023, 00:35
TBT wrote:
Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(310\pi\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees


TBT - The question is clearly flawed.

The question states that the radius is 10 inches. The circumference of the circle is \(2 \pi * 10\) = \(20\pi\)

I am surprised to see that the length of the arc ABC is \(310\pi\), which is more than 15 times the length of the circumference :dazed

Please review the question and post the correct version.
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   20 Mar 2023, 01:09
gmatophobia wrote:
TBT wrote:
Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(310\pi\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees


TBT - The question is clearly flawed.

The question states that the radius is 10 inches. The circumference of the circle is \(2 \pi * 10\) = \(20\pi\)

I am surprised to see that the length of the arc ABC is \(310\pi\), which is more than 15 times the length of the circumference :dazed

Please review the question and post the correct version.


My bad. It was a typo. Length of the arc is: 10 pie /3
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   20 Mar 2023, 01:19
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TBT wrote:
Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(\frac{10 \pi }{ 3 }\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees


Let the angle \(\angle\)AOC = x

\(\frac{x}{360} * 2\pi*r = \frac{10\pi }{ 3}\)

\(\frac{x}{360} * 2\pi*10 = \frac{10\pi }{ 3}\)

Upon solving x = 60

Option D.
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   20 Mar 2023, 06:59
TBT wrote:
Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(\frac{10 \pi }{ 3 }\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees


angle AOC/360=length of the arc ABC/circumference of the circle

Length of the arc =10pi/3
circumference of the circle =2*pi*10=20pi
We will have to find out the value of angle AOC

Hence,
Angle AOC=(10pi/3*20pi)*360=60 degrees.Ans d
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink] New post   20 Mar 2023, 07:53
TBT wrote:
Points A, B, and C lie on a circle whose radius is 10 inches. If O is the center of the circle and the length of arc ABC is \(\frac{10 \pi }{ 3 }\) what is the degree measure of \(\angle\)AOC?

a. 15 degrees

b. 30 degrees

c. 45 degrees

d. 60 degrees

e. 90 degrees

\(θ \frac{π}{180}*10 = \frac{10π}{3}\)

So, \(θ = 60\)°, Answer must be (D) 60°
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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink]
20 Mar 2023, 07:53
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