Question

the circle has center (o), and the measure of angle (aoc) is (120^{circ}). the length of minor arc (overset{\frown}{ac}) is what fraction of the circumference of the circle? (the number of degrees of arc in a circle is 360.)

Explanation:

Step1: Recall arc - length formula

The length of an arc $s = r\theta$ (where $\theta$ is in radians) or $s=\frac{\theta}{360}\times2\pi r$ (where $\theta$ is in degrees). The circumference of a circle is $C = 2\pi r$.

Step2: Calculate the fraction

The fraction of the arc - length to the circumference is $\frac{\text{arc length}}{\text{circumference}}=\frac{\frac{120}{360}\times2\pi r}{2\pi r}$. The $2\pi r$ terms cancel out, and $\frac{120}{360}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$