Q12. - Geometry

Question

Use a compass to draw a large $\odot o.$ Draw a central $\angle AOB.$.

    a. draw three other points $P,Q$ and $R$ that are on $\odot o$but not on $\stackrel{⏜}{AB}$.

        then draw $\angle APB,\angle AQB$ and $\angle ARB$.

    b. Use a protractor to find  $m\angle AOB,m\angle APB,m\angle AQB$ and  $m\angle ARB$.

    c. What is the relationship between   $m\angle APB,m\angle AQB$ and  $m\angle ARB?$  

       What is the relationship between $m\angle AOB$ and $m\angle APB?$

Step-by-Step Solution

Answer

(a)

The final answer  is

(b)

The final answer  is 

$\begin{array}{c}\angle APB=\angle AQB\\ =\angle ARB\\ ={29}^{\circ }\end{array}$

(c)

The final answer is all are equal.

$\begin{array}{c}\angle APB=\angle AQB\\ =\angle ARB\\ ={29}^{\circ }\end{array}$

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

Step 1. Given information:

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

$P,Q$ and $R$are the points on the circle but on the arc $\stackrel{⏜}{AB}.$ 

Step 2. Concept used:

We use compass to make a circle.

Then we make the angle

Step 3. Applying the concept:

At first, using a compass make a circle $\odot o.$

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

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

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

Step 1. Given information:

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

$P,Q$ and $R$are the points on the circle but on the arc $\stackrel{⏜}{AB}.$ 

Step 2. Concept used:

  Basic concept of geometry and angles. 

Step 3. Applying the concept:

At first, using a compass make a circle $\odot o.$

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

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

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

Use the protector placing on $P,Q$and $R$measuring the values of $\angle APB,\angle AQB$ and $\angle ARB$,

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

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

Step 1. Given information:

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

$P,Q$ and $R$are the points on the circle but on the arc $\stackrel{⏜}{AB}.$         

Step 2. Concept used:

Basic concept of geometry and angles.

Step 3. Applying the concept:

At first, using a compass make a circle $\odot o.$

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

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

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

Use the protector placing on $P,Q$ and $R$measuring the values of $\angle APB,\angle AQB$ and $\angle ARB$,

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

 The relation between  $\angle APB,\angle AQB$ and $\angle ARB$is 

 $\begin{array}{c}\angle APB=\angle AQB\\ =\angle ARB\\ ={29}^{\circ }.\end{array}$

 

Now, from the following figure, $\angle AOB$and $\angle APB$ are,  

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

Hence, the measurement of the angle are which concludes the relation $\begin{array}{l}\angle APB=\angle AQB\\ =\angle ARB\\ ={29}^{\circ },\end{array}$

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