Question #N227
A circle with center O has a radius of 5. If point A lies on the circle and $\angle AOB = 120^\circ$, what is the length of minor arc AB?
A. $\frac{10\pi}{3}$
B. $\frac{20\pi}{3}$
C. $\frac{10\pi}{6}$
D. $\frac{5\pi}{3}$
Correct Answer is: A
The length of an arc is a fraction of the circumference of the circle, determined by the central angle of the arc. The fraction is the ratio of the arc's central angle to 360 degrees. In this case, the ratio is $\frac{120^\circ}{360^\circ} = \frac{1}{3}$. The circumference of the circle is given by $2\pi r = 2\pi (5) = 10\pi$. Therefore, the length of minor arc AB is $\frac{1}{3} \cdot 10\pi = \frac{10\pi}{3}$.