Chapter 12, Problem 17CUR

To determine

To find: The length of AB if the radius of circle is 8.

Answer to Problem 17CUR

The length of AB is 8.

Explanation of Solution

Given information: The center of a circle is O and radius is 8. The arc AB lies on the circle and $m\stackrel{⌢}{AB}=60$ .

Calculation:

It is given that the arc AB lies on $\odot O$ with $m\stackrel{⌢}{AB}=60$ . The radius is 8.

The formula to find the arc length of a circle is:

  $\text{arc length}=\text{radius}\cdot \text{central angle}\cdot \frac{\pi }{180}$

So, the length of AB can be calculated as:

  $\stackrel{⌢}{AB}=\text{radius}\cdot m\stackrel{⌢}{AB}\cdot \frac{\pi }{180}$

Substitute 8 for radius and 60 for $m\stackrel{⌢}{AB}$ in the above formula.

  $\begin{array}{c}\stackrel{⌢}{AB}=\text{8}\cdot 60\cdot \frac{\pi }{180}\\ =8\cdot \left(1.04\right)\\ =8\end{array}$

Therefore, the length of AB is 8.