Chapter 9.2, Problem 12PSB

a

To determine

To find:The measure of arc JK

Answer to Problem 12PSB

The value of $m\stackrel{⌢}{JK}={120}^0$

Explanation of Solution

Given information:The following measures have been given

Q is the center of circle

HM is a diameter of the circle

  $m\stackrel{⌢}{HJ}={20}^0$

  $m\stackrel{⌢}{MK}={40}^0$

Formula used:Linear addition of angles is done

Calculation:We know that as HM is the diameter,

  $m\stackrel{⌢}{HJ}+m\stackrel{⌢}{MK}+m\stackrel{⌢}{JK}={180}^0$

Hence, substituting the values of arcs HJ and MK in the equation above, we get

  $m\stackrel{⌢}{JK}={120}^0$

b

To determine

To find:The length of arc JK

Answer to Problem 12PSB

The value of $\stackrel{⌢}{JK}=9\pi$

Explanation of Solution

Given information:The following measures have been given

Q is the center of circle

Circumference of the circle is $C=27\pi$

  $m\stackrel{⌢}{JK}={120}^0$

Formula used:The length of any arc will be

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

Calculation:We know that as Circumference of the circle is $27\pi$ ,

  $27\pi =2\pi r\to r=\frac{27}{2}$

Also, now we can say that the length of any arc will be

  $\stackrel{⌢}{JK}=2\pi r\frac{{120}^0}{{360}^0}$

Hence, substituting the values of radius the equation here, we get

  $\stackrel{⌢}{JK}=9\pi$

c

To determine

To find:The length of HM

Answer to Problem 12PSB

The value of $HM=27$

Explanation of Solution

Given information:The following measures have been given

Q is the center of circle

HM is a diameter of the circle

  $m\stackrel{⌢}{HJ}={20}^0$

  $m\stackrel{⌢}{MK}={40}^0$

Formula used:The relation between diameter and radius is

  $d=2r$

Where d is the diameter and ris the radius.

Calculation:We know that as HM is the diameter,

  $HM=2r$

Hence, substituting the values of radius in the equation above, we get

  $HM=27$