NCERT Solutions For Class 9 Maths Chapter 9 Exercise 9.3 Circles - PDF Download

The NCERT solutions for class 9 maths chapter 9 ex 9.3 has questions based on the topics and theorems of the angle subtended by an arc of a circle and cyclic quadrilaterals. This topic includes five theorems, all of which are covered by NCERT solutions in chapter 9 of class 9 maths. Ex 9.3 class 9 maths chapter 9 includes all of these theorems, as well as proofs to assist students in understanding this fundamental topic and its applications. The cyclic quadrilaterals and the sum of its angles are explained with examples to make it easy to understand.

Class 9 maths chapter 9 exercise 9.3 NCERT solutions consist of 12 questions based on these concepts and theorems. The NCERT solutions for chapter 9 in class 9 maths ex 9.3 are available here in PDF format and can be downloaded for free. Ex 9.3 class 9 maths solutions have been developed by expert teachers from eSaral and are easy to understand. These solutions can be used by students as a reference to score good marks in exams.

Topics Covered in Exercise 9.3 Class 9 Mathematics Questions

Exercise 9.3 is based on the concepts included in the chapter which mainly covers the concept of the angle subtended by an arc of a circle and the cyclic quadrilaterals. You can check these concepts in detail mentioned below.

1. Angle Subtended by an Arc of a Circle 

• If two chords of a circle are equal, then their corresponding arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.
• Congruent arcs (or equal arcs) of a circle subtend equal angles at the centre

These above-mentioned statements are true to the reference of angle subtended by an arc of a circle. You can find the detailed solutions of these statements in chapter 9 class 9 maths textbook. 

Here are some important theorems associated with the topic angle subtended by an arc of a circle.

• Theorem 9.7: The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

• Theorem 9.8: Angles in the same segment of a circle are equal.

• Theorem 9.9: If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle 

    2. Cyclic Quadrilaterals - If all the vertices of a quadrilateral lie in the circumference of a circle, then it is called a cyclic quadrilateral.

Here are some important theorems associated with the topic cyclic quadrilaterals.

• Theorem 9.10: The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

• Theorem 9.11: If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic. 

Tips for Solving Exercise 9.3 Class 9 Chapter 9 Circles 

Regular practice of the questions and examples included in NCERT solutions class 9 maths chapter 9 ex 9.3 can be beneficial in achieving a comprehensive solution-oriented approach to solving each question. Here are some important tips on how to solve questions to score high marks.

1. Students will have a thorough understanding of the theorems when they follow the step by step solution to the questions provided in NCERT solutions class 9 chapter 9 exercise 9.3.

2. Students should also write the steps of solutions, as the majority of the questions require proof of the statements. This will enable them to understand the application of the concept.

Importance of Solving Ex 9.3 Class 9 Maths Chapter 9 Circles

Ex 9.3 class 9 maths chapter 9, students will receive significant advantages for mathematics after solving the problems from NCERT solutions.

1. The main goal of this exercise is to assist students in developing a clear comprehension of the circle theorems relating to angles subtended by the arc of the circle and the cyclic quadrilaterals which gives clear understanding of these topics.

2. Ex 9.3 class 9 problems are solved step by step. This helps the students to follow the problem solving process and comprehend the concepts. 

3. Ex 9.3 class 9 solutions are available in downloadable PDF format, allowing students to access and download them offline for ease of study.

4. You can solve all the questions from Ex 9.3 in the final exam after solving several questions in NCERT solutions.

Frequently Asked Questions

Question 1. Write the theorem related to cyclic quadrilaterals?

Answer 1. If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic. 

Question 2. What are cyclic quadrilaterals?

Answer 2. If all the vertices of a quadrilateral lie in the circumference of a circle, then it is called a cyclic quadrilateral.