📑 Table of Contents
📖 About Class 9 Maths Chapter 5 Exercise 5.2
Class 9 Maths Chapter 5 Exercise 5.2 is the second exercise of Chapter 5 – I’m Up and Down, and Round and Round from the latest NCERT Ganita Manjari (2026). This exercise focuses on the relationship between chords and the angles they subtend at the centre of a circle, with questions based on the theorems introduced in this part of the chapter.
This page provides the complete Exercise Set 5.2 in a clear, step-by-step format, including the relevant theorem proofs and question-wise solutions. The presentation follows a student-friendly CBSE answer-writing approach and is designed for classroom practice, homework, self-study and revision.
🎯 Exercise Snapshot
- Complete Exercise Set 5.2 coverage.
- NCERT-based solutions for both exercise questions.
- Relevant theorem statements and step-by-step proofs.
- Central-angle and chord-based explanations.
- Theorem proofs presented step by step.
- Question-wise solutions with clear reasoning.
- Students studying the new Ganita Manjari textbook.
- Homework and classroom practice.
- Revision and CBSE examination preparation.
Since CA, CB, CD and CE are radii of the same circle,
Therefore, corresponding angles of congruent triangles are equal by CPCT.
Since CA, CB, CD and CE are radii of the same circle,
Therefore, corresponding sides of congruent triangles are equal by CPCT.
Now, OA and OB are radii of the same circle. Therefore,
A triangle having two equal sides is called an isosceles triangle.
So, when the question gives us an equal chord or an equal central angle, we can use SSS or SAS congruence to prove the required result.
📝 Class 9 Maths Chapter 5 Exercise 5.2 Solutions
Solve every question of Class 9 Maths Chapter 5 Exercise 5.2 with clear, step-by-step NCERT Ganita Manjari (2026) solutions. This exercise focuses on important ideas involving central angles, chords, equal chords, and the related theorems. The theorem proofs and question-wise solutions are presented in a simple, student-friendly CBSE answer-writing style with clear reasoning, making this page useful for classroom work, homework, revision, and examination preparation.
📚 Continue Learning
Congratulations! You have completed Class 9 Maths Chapter 5 Exercise 5.2 Solutions. You have now worked through the second exercise of Chapter 5 – I’m Up and Down, and Round and Round, including central angles, chords and the related theorems. Continue your learning journey by revisiting Exercise 5.1, exploring the complete chapter, or moving to the next exercise when it becomes available.
📖 Explore More Class 9 Maths Chapters
❓ Frequently Asked Questions
Find answers to common student questions about Class 9 Maths Exercise 5.2. These FAQs clarify the central-angle concept, the relationship between chords and angles at the centre, and the theorem-based reasoning used in the exercise.
What is the main focus of Exercise Set 5.2?
Exercise Set 5.2 focuses on the angle subtended by a chord at the centre of a circle and the relationship between chords and these central angles. The exercise also uses the properties of the triangles formed by joining the centre to the endpoints of a chord.
What is a central angle in this exercise?
When the endpoints of a chord are joined to the centre of the circle, the angle formed at the centre is the angle subtended by that chord at the centre. For a chord AB and centre O, this angle is written as ∠AOB.
What is the theorem about equal chords and central angles?
The theorem states that equal chords of a circle subtend equal angles at the centre of the circle. In the proof, the radii and equal chords provide three pairs of equal sides, so the two triangles are proved congruent by SSS. Corresponding angles are then equal.
What is the converse theorem used in Exercise 5.2?
The converse states that chords of a circle that subtend equal angles at the centre are equal. Its proof uses the equal radii together with the equal central angles to establish triangle congruence by SAS. Corresponding chords are then equal.
Why does joining a chord to the centre form an isosceles triangle?
If a chord AB is joined to the centre O, the segments OA and OB are radii of the same circle. Therefore, OA = OB. Since two sides of triangle OAB are equal, the triangle is isosceles.
Why is SSS congruence used in the equal-chords theorem?
For two equal chords, the corresponding segments from the centre are radii and are therefore equal. Together with the equal chords, this gives three pairs of equal corresponding sides. Hence, the triangles can be proved congruent by SSS.
Why is SAS congruence used in the converse theorem?
In the converse theorem, the corresponding radii are equal because they belong to the same circle, and the included central angles are given equal. Thus, two corresponding sides and the included angle are equal, so SAS congruence proves that the triangles are congruent.
Are these Class 9 Maths Exercise 5.2 Solutions based on Ganita Manjari 2026?
Yes. This page follows Chapter 5 – I’m Up and Down, and Round and Round from the NCERT Ganita Manjari (2026) textbook and covers the material and questions of Exercise Set 5.2. The page presents the relevant theorem proofs and the two exercise questions in a step-by-step, student-friendly format.
Rakesh Kumar Singh
Founder, Maths Gurukulam & Newton Study Point
Teaching CBSE Mathematics Since 2006
These Class 9 Maths Chapter 5 Exercise 5.2 Solutions are carefully prepared according to the latest NCERT Ganita Manjari (2026) and the CBSE curriculum. The solutions follow a clear, step-by-step approach to help students understand the central-angle and chord relationships, theorem-based reasoning, and problem-solving methods used in Exercise 5.2.