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Re: Points A, B, and C lie on a circle whose radius is 10 inches. If O is [#permalink]
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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]
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]
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]
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