Question

in circle o, the length of minor arc ab is what fraction of the circumference? 2/7 1/5 2/3 1/3

Explanation:

Step1: Recall the formula for arc length

The formula for the length of an arc \(l\) is \(l=\frac{\theta}{360^{\circ}}\times C\), where \(\theta\) is the central angle and \(C\) is the circumference.

Step2: Substitute the given central angle

Given \(\theta = 120^{\circ}\), we substitute into the formula. The fraction of the arc length to the circumference is \(\frac{l}{C}=\frac{\theta}{360^{\circ}}\).
Substituting \(\theta = 120^{\circ}\), we get \(\frac{120^{\circ}}{360^{\circ}}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\) (corresponding to the last option)