NCERT Solutions for Class 9 Maths Chapter 10 – Circles Exercise 10.2 have been presented here for students to prepare thoroughly for the second term exam. It has been designed by our experts with respect to 9th standard NCERT syllabus and guidelines (2020-21), prescribed by CBSE. These solutions of Class 9 Maths subject, are helpful for students, to do their homework assigned in their schools and also score good marks in the first and second term exam.
Access Other Exercise Solutions of Class 9 Maths Chapter 10- Circles
- Exercise 10.1 Solutions : 2 Question ( 2 Short)
- Exercise 10.2 Solutions : 2 Question ( 2 Long)
- Exercise 10.3 Solutions : 3 Question ( 3 Long)
- Exercise 10.4 Solutions : 6 Question ( 6 Long)
- Exercise 10.5 Solutions : 12 Question ( 12 Long)
- Exercise 10.6 Solutions : 10 Question ( 10 Long)
Access Answers to NCERT Class 9 Maths Chapter 10 – Circles Exercise 10.2
1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
To recall, a circle is a collection of points whose every point is equidistant from its centre. So, two circles can be congruent only when the distance of every point of both the circles are equal from the centre.
For the second part of the question, it is given that AB = CD i.e. two equal chords.
Now, it is to be proven that angle AOB is equal to angle COD.
Consider the triangles ΔAOB and ΔCOD,
OA = OC and OB = OD (Since they are the radii of the circle)
AB = CD (As given in the question)
So, by SSS congruency, ΔAOB ΔCOD
∴ By CPCT we have,
AOB = COD. (Hence proved).
2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Consider the following diagram-
Here, it is given that AOB = COD i.e. they are equal angles.
Now, we will have to prove that the line segments AB and CD are equal i.e. AB = CD.
In triangles AOB and COD,
AOB = COD (as given in the question)
OA = OC and OB = OD (these are the radii of the circle)
So, by SAS congruency, ΔAOB ΔCOD.
∴ By the rule of CPCT, we have
AB = CD. (Hence proved).
It consists of two questions based on two theorems, which are explained before this exercise. They are:
Theorem 1: Equal chords of a circle subtend equal angles at the centre.
Theorem 2: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
Students have to prove the given scenarios with respect to above-given theorems. Therefore, through solutions for Class 9 Maths Chapter 10, we have given a brief explanation for each question.
The questions in Exercise 10.2 have mid-length answers, which students can easily grasp. Solve NCERT solutions where problems are resolved in a comprehensive way following each and every step.