NCERT Solutions for Class 9 Maths Chapter 9 Circles - PDF Download

NCERT solutions for class 9 maths chapter 9 is a great way to help you learn the concept of circles. A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane. This boundary is called the circumference. The line connecting the center of the circle to any point on the circumference is called the radius. The area enclosed within the arc of the circle is referred to as the area of a circle. These properties of a circle are essential for you to grasp an understanding of circles. Thus, It is essential for students to have a thorough comprehension of this topic. 

The topics mentioned in NCERT solutions for class 9 chapter 9 Circles are the foundation for learning many complex topics. With proper practice of all questions in these NCERT solutions, students will get to know the concepts related to Circles like Circumference, Diameter, Chord, Arc, Secant, Sector, Segment, Subtended Angle, etc. In addition to learning the fundamentals of this topic, students will also be able to put their knowledge into practice in real situations.

NCERT solutions  for class 9 maths chapter 9 are prepared by a mathematics experts team to help students develop analytical thinking. The questions included in these exercises effectively provide knowledge of all aspects related to circles. The NCERT solutions for class 9 maths chapter 9 Circles are available in PDF format that can be downloaded for free. It helps students to resolve their doubts and improve their exam scores. Students can get a variety of questions to get enough practice.

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Important Topics covered in Chapter 9 - Circles

Below are the main topics covered in our NCERT solutions for class 9 maths chapter 9 Circles.

NCERT solutions for class 9 maths chapter 9 will provide students with step by step instructions and explanations on each of the following topics:

9.1 Angle Subtended by a Chord at a Point - In this section, students are asked to draw a card in a circle. The line is then extended to another point that connects two line segments. Inside the circle, it creates a triangle. This is also referred to as the angle subtended at a point by a chord. If the chord lengths are equal, then the angles of the chords are equal, and vice versa.

9.2 Perpendicular from the Centre to a Chord - In this part of the lesson, students can practice drawing a perpendicular from the center of the chord.

9.3  Equal Chords and their Distances from the Centre - This part of the NCERT solutions for class 9 maths chapter 9 states that the length of a perpendicular is the distance between a point and a line. If the point is on a line, then the distance from the line to the point is zero. 

9.4 Angle Subtended by an Arc of a Circle - NCERT solutions for class 9 maths chapter 9 is entirely concerned with Circles. if we draw two arcs congruent from the center, then they have to be equal. 

9.5 Cyclic Quadrilaterals - If all the vertices of the quadrilateral are in the circle, then the quadrilateral is referred to as a Cyclic Quadrilateral.

Important Theorems Covered In NCERT solutions for Class 9 Maths Chapter 9 - Circles

NCERT solutions for class 9 maths chapter 9 Circles have included some important theorems.

• 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. 
• Theorem 3 : The perpendicular from the centre of a circle to a chord bisects the chord. 
• Theorem 4 : The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
• Theorem 5 : Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres). 
• Theorem 6 : Chords equidistant from the centre of a circle are equal in length.
• Theorem 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 8 : Angles in the same segment of a circle are equal.
• Theorem 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 (i.e. they are concyclic).
• Theorem 10 :The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.
• Theorem 11 : If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

NCERT Solutions for Class 9 Maths Chapter 9 Exercises

NCERT solutions for class 9 maths chapter 9 provide comprehensive solutions to all the exercises. You can use it as a reference to improve your preparation and perform better in the exams.

Benefits of Downloading The NCERT Solutions for Class 9 Maths Chapter 9 - Circles

In this section, you will learn about the many benefits of downloading and using NCERT solutions in order to master the topics mentioned in this chapter.

1. In NCERT solutions, our experienced teachers have broken down the chapter into various parts, allowing students to gain a deeper understanding of the concepts.
2. Chapter 9 of the NCERT solutions offers comprehensive solutions to all questions to ensure a thorough understanding of the topics.
3. NCERT solutions help students learn the best ways to solve problems. This knowledge helps students manage their time during exams.
4. The eSaral NCERT solutions help students feel more confident, boost their learning skills, get through complicated topics easily.

Frequently Asked Questions

Question 1. What are the most important topics covered in NCERT solutions for class 9 maths chapter 9 ?

Answer 1.  NCERT solutions for class 9 maths chapter 9 Circles includes the following topics:

1. Angle Subtended by a Chord at a Point
2. Perpendicular from the Centre to a Chord
3. Equal Chords and their Distances from the Centre
4. Angle Subtended by an Arc of a Circle
5. Cyclic Quadrilaterals

Question 2. How can I solve the problems associated with chapter 9 Circles ?

Answer 2. Before trying to solve any problem, you need to make sure that the fundamental concepts are clear in your mind. Students can use NCERT solutions provided by eSaral’s mathematics experts for class 9 maths chapter 9 Circles to solve the problems correctly and understand the concepts. These solutions are also available on the eSaral website. eSaral’s mathematics expert teachers solve these problems as logically and easily as possible.