# NCERT Solutions for Class 9 Maths Chapter 9 Circles

## NCERT Solutions for Class 9 Maths Chapter 9 Circles

NCERT solutions Chapter 9 Circles is a resource that has been thoughtfully prepared to help students ace a very integral topic. Class 9 maths chapter 9 Circles deals with numerous essential topics like the properties of the circles and manipulating lines and angles within the circles. There are numerous questions based on these topics that can pose a serious obstacle for anyone studying them so it is for the benefit of such students that we have compiled all the answers of each exercise in Class 9 maths chapter 9 Circles.

Students will be exposed to a broad spectrum of concepts in Class 9 maths chapter 9 Circles which may be tough to learn initially. The easiest way to grasp these ideas would be via understanding the questions given in the exercises of chapter 9. For this purpose students will find NCERT solutions class 9 maths chapter to be of great utility.

## Theorems included in NCERT Class 9 Chapter 9 Solutions

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: f 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.

### What is the Importance of NCERT Solutions for Class 9 Maths Chapter 9 Circles?

Students can expect questions along the lines of finding unknown angles, proving the relations given in the question and even word problems based on the concepts. The possible questions that students can encounter in an exam have immense variation and this may also intimidate them while studying the chapter. NCERT Solutions for Class 9 Maths Chapter 9 have been designed to systematically guide the students to the answer to each problem in the NCERT textbook which will make them much more at ease with the topic and reduce their fears surrounding the content. These solutions also promote active recall which is the most efficient strategy for revising any topic.

### How are NCERT Solutions for Class 9 Maths Chapter 9 helpful for Class 9 students?

Students can expect questions along the lines of finding unknown angles, proving the relations given in the question and even word problems based on the concepts. The possible questions that students can encounter in an exam have immense variation and this may also intimidate them while studying the chapter. NCERT Solutions for Class 9 Maths Chapter 9 have been designed to systematically guide the students to the answer to each problem in the NCERT textbook which will make them much more at ease with the topic and reduce their fears surrounding the content. These solutions also promote active recall which is the most efficient strategy for revising any topic.

### Why should we follow NCERT Solutions for Class 9 Maths Chapter 9?

NCERT Solutions Class 9 Maths Chapter 9 Circles are very comprehensive, covering every exercise and every sub-part found in the chapter. Additionally these solutions have been prepared by skilled and qualified individuals who prioritise the understanding and learning of the students. With these two aims in mind the class 9 maths NCERT solutions chapter 9 becomes the best way to become familiar with the concepts present in the NCERT curriculum. Furthermore these solutions have been designed to be in line with the updated NCERT book content ensuring the accuracy of the information provided.

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