Introduction, Theorems & Ex 9.1 Full Explanation | NCERT Maths | Class 9 | कक्षा 9 Circles परिचय

Описание: Welcome to Infinix Classes – Maths by Faiz Sir!
In this video, we begin Chapter 9 – Circles (NCERT Class 9) with a clear and complete introduction, important theorems, proofs, and full Exercise 9.1 solutions.

✔️ Angle Subtended by a Chord at a Point
✔️ Theorem 9.1: Equal chords subtend equal angles at the centre
✔️ Theorem 9.2: If angles subtended at centre are equal → chords are equal
✔️ Proofs explained step-by-step
✔️ Exercise 9.1 NCERT – All questions solved

Perfect for CBSE Class 9 students, school exams, periodic tests, and maths revision.

📘 Topics Covered in This Video:
🔹 Theory & Introduction

What is a circle?

What is a chord?

Angle subtended by a chord

Centre angle vs inscribed angle

Congruent circles concept

🔹 Theorem 9.1 (with proof)

Equal chords subtend equal angles at the centre.

🔹 Theorem 9.2 (with proof)

If centre angles are equal, the chords must be equal.

🔹 Exercise 9.1 Solutions

Q1. Equal chords of congruent circles subtend equal angles – prove
Q2. If angles subtended at centres are equal, chords are equal – prove

Faiz Sir explains with diagrams, logic, and clarity—best for exam preparation.

⭐ Why Watch This Video?

Simple language

NCERT based

Diagram-wise explanation

100% exam-oriented

Helps build strong geometric concepts

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More chapters of Class 9 Maths coming soon.



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CHAPTER - 9 | Circles | By: Faiz Sir, M. Sc. Maths with CS | Class – 9 | NCERT


Angle Subtended by a Chord at a Point:
किसी बिंदु पर जीवा द्वारा बनाया गया कोण:


Theorem 9.1 : Equal chords of a circle subtend equal angles at the centre.
एक वृत्त की समान जीवाएँ केंद्र पर समान कोण अंतरित करती हैं।


Theorem 9.2 : If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
यदि किसी वृत्त की जीवाओं द्वारा केंद्र पर अंतरित कोण बराबर हों, तो जीवाएँ भी बराबर होती हैं।



EXERCISE 9.1

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.
याद कीजिए कि दो वृत्त सर्वांगसम होते हैं यदि उनकी त्रिज्याएँ समान हों। सिद्ध कीजिए कि सर्वांगसम वृत्तों की समान जीवाएँ उनके केंद्रों पर समान कोण अंतरित करती हैं।


2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
सिद्ध कीजिए कि यदि सर्वांगसम वृत्तों की जीवाएँ अपने केन्द्रों पर समान कोण अंतरित करती हैं, तो जीवाएँ समान होती हैं।