Question

in circle b, bc = 3 and m∠cbd = 80°. find the length of cd. 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 \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

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

Given that \(\theta = m\angle CBD=80^{\circ}\) and \(r = BC = 3\).

Step3: Substitute the values into the formula

Substitute \(\theta = 80\) and \(r = 3\) into \(s=\frac{\theta}{360}\times2\pi r\).

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Answer:

\(\frac{4}{3}\pi\)