Question

in circle a, ab = 11 and m∠bac = 20°. find the length of (overparen{bc}). express your answer as a fraction times π (in simplest form).

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle is \(s=\frac{\theta}{360^{\circ}}\times2\pi r\), where \(\theta\) is the central angle and \(r\) is the radius of the circle.

Step2: Identify the values of \(\theta\) and \(r\)

Given that \(\theta = m\angle BAC=20^{\circ}\) and \(r = AB = 11\).

Step3: Substitute the values into the formula

Substitute \(\theta = 20^{\circ}\) and \(r = 11\) into the arc - length formula:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{11\pi}{9}\)