NCERT Solutions for Class 9 Maths Exercise 10.5 Circles updated for CBSE and State board students session 2022-2023. Grade 9 Maths Solutions are available in Hindi and English Medium online and offline mode. Students can download PDF and Video to use it offline without internet.

## NCERT Solutions for Class 9 Maths Exercise 10.5

### Theorems related to Exercise 10.5 Class 9

This is the most interesting and exciting of the present topic. Few of the interesting things that we are going to study are, if two chords of a circles are equal in length, then there corresponding arcs are congruent.

Conversely if two arcs are “congruent”, then their corresponding chords must be equal. Re –collect the meaning of the word “congruent” and the word “segment”.

#### Congruence of Circles in Class 9 Exercise 10.5

The term congruent means that if two figures are placed one above the other, they will have similar shape. i.e., the shape will be exactly the same. The term segment means the region between a chord and either of its arcs.

You may also say that a segment is the part of the whole circle. The entire circle can be divided into two segment minor and major. These two may be equal or unequal. They can equal only if both the parts are semicircles.

##### Important theorems of Exercise 10.5 in 9th Maths

Another interesting feature to be learn in this exercise that theorem 10.8 this says that the angles subtended by an arc at the center of the circle is double the angle subtended by it at any point on remaining part of the circle.

One of the practical ways to learn this topic or for that matter any topic in geometry is to draw the required figure and see the proof by measuring the angles.

###### Application of theorem in questions of Exercise 10.5

As they say in English, that the taste of pudding is in the eating. So, if you draw the required figure check the angles.

You will really find that the angles at the centre is double the measure of angle on the remaining part of it. Exercise 10.5 contains 8 application based questions and they should be practiced by drawing proper diagrams.