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505-555 (Easy)|   Geometry|      
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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 Updated on: 20 Mar 2023, 01:13
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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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

88% (01:33) correct 12% (01:43) wrong based on 41 sessions

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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
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gmatophobia
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Points A, B, and C lie on a circle whose radius is 10 inches. If O is 20 Mar 2023, 00:35
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TBT
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
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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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TBT
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Points A, B, and C lie on a circle whose radius is 10 inches. If O is 20 Mar 2023, 01:09
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gmatophobia
TBT
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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My bad. It was a typo. Length of the arc is: 10 pie /3
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Points A, B, and C lie on a circle whose radius is 10 inches. If O is 20 Mar 2023, 01:19
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TBT
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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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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Points A, B, and C lie on a circle whose radius is 10 inches. If O is 20 Mar 2023, 06:59
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TBT
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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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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Points A, B, and C lie on a circle whose radius is 10 inches. If O is 20 Mar 2023, 07:53
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TBT
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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\(θ \frac{π}{180}*10 = \frac{10π}{3}\)

So, \(θ = 60\)°, Answer must be (D) 60°
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