Chapter 9.3, Problem 12WE

a.

To determine

the given figure from the given information.

Explanation of Solution

Given:

Draw a circle $\odot O$ and draw a central angle $\angle AOB$ .

  $P,Q\text{ and }R$ are the points on the circle but not on the arc $\stackrel{⌢}{AB}$ .

At first, using a compass make a circle $\odot O$ ,

  

Now, making a central angle $\angle AOB$ ,

  

  $P,Q\text{ and }R$ are the points on the circle but not on $\stackrel{⌢}{AB}$ ,

  

Conclusion:

The above figure is the required figure that can be drawn from the given information.

b.

To determine

the measurements of the angles.

Answer to Problem 12WE

  $\angle APB=\angle AQB=\angle ARB=29°$ .

Explanation of Solution

Given:

Draw a circle $\odot O$ and draw a central angle $\angle AOB$ .

  $P,Q\text{ and }R$ are the points on the circle but not on $\stackrel{⌢}{AB}$ .

Concept used:

Basic concept of geometry and angles.

At first, using a compass make a circle $\odot O$ ,

  

Now, make a central angle $\angle AOB$ ,

  

  $P,Q\text{ and }R$ are the points on the circle but not on $\stackrel{⌢}{AB}$ ,

  

Now, to find the value of $\angle APB,\angle AQB\text{ and }\angle ARB$ ,

  

use the protector placing on $P,Q\text{ and }R$ measuring the values of $\angle APB,\angle AQB\text{ and }\angle ARB$ ,

  

So, the values of $\angle APB,\angle AQB\text{ and }\angle ARB$ are all same, that is, $29°$ .

Conclusion:

Therefore, the measurements of the angle are $29°$ , which concludes that all the angles are equal.

c.

To determine

the relation between the angles.

Answer to Problem 12WE

  $\angle APB=\angle AQB=\angle ARB=29°$ , that is, all are equal.

There is no such relation between $\angle AOB\text{ and }\angle APB$ .

Explanation of Solution

Given:

Draw a circle $\odot O$ and draw a central angle $\angle AOB$ .

  $P,Q\text{ and }R$ are the points on the circle but not on $\stackrel{⌢}{AB}$ .

Concept used:

Basic concept of geometry and angles.

At first, using a compass make a circle $\odot O$ ,

  

Now, make a central angle $\angle AOB$ ,

  

  $P,Q\text{ and }R$ are the points on the circle but not on $\stackrel{⌢}{AB}$ ,

  

Now, to find the values of $\angle APB,\angle AQB\text{ and }\angle ARB$ ,

  

use the protector placing on $P,Q\text{ and }R$ measuring the value of $\angle APB,\angle AQB\text{ and }\angle ARB$ ,

  

So, the values of $\angle APB,\angle AQB\text{ and }\angle ARB$ are all same, that is, $29°$ .

The relation between $\angle APB,\angle AQB\text{ and }\angle ARB$ is $\angle APB=\angle AQB=\angle ARB=29°$ .

Now, from the following figure, $m\angle AOB\text{ and }m\angle APB$ are,

  

So, there is no relation between $\angle AOB\text{ and }\angle APB$ as $\angle AOB$ is $59°$ , which is greater than $\angle APB$ .

Conclusion:

Hence, the measurements of the angle are $29°$ , which concludes the relation $\angle APB=\angle AQB=\angle ARB=29°$ , and there is no such relation between $\angle AOB\text{ and }\angle APB$ as $\angle AOB$ is $59°$ , which is greater than $\angle APB$ .