Chapter 9.2, Problem 16PSB

a

To determine

To find:The measure of arc JK

Answer to Problem 16PSB

The measure of arc JK is ${90}^0$

Explanation of Solution

Given information:The following information has been given

O is the center of the circle

  $\angle JHK={45}^0$

We know that the arc JK will subtend double the angle of what it subtended on the circumference on the center of the circle. Hence, we can say that the measure from the center of the circle will be

  $m\stackrel{⌢}{JK}=2\angle JHK=2({45}^0)={90}^0$

b

To determine

To find:The length of arc JK

Answer to Problem 16PSB

The length of arc JK is $12.566$

Explanation of Solution

Given information:The following information has been given

O is the center of the circle

  $\angle JHK={45}^0$

  $m\stackrel{⌢}{JK}={90}^0$

Formula used:The length of any arc will be

  $\stackrel{⌢}{JK}=2\pi r\frac{\theta }{{360}^0}$

Calculation:first of all, we find the radius of the circle as the distance between points O and K. hence, we get

  $r=6$

The length of the arc JK can be calculated as

  $\stackrel{⌢}{JK}=2\pi r\frac{{90}^0}{{360}^0}=\frac{12\pi }{4}=12.566$