# CBSE Class 9 Maths Circles

As per CBSE Class, 9 Syllabus prescribed by NCERT, the chapter on Circles covers its introduction, the angles subtended by the chord, the concept on the perpendicular from centre to chord, the properties of equal chords and the concepts on Cyclic quadrilaterals.

CBSE Class 9 Introduction to circles helps understand the basics pre-requisites on circles to solve application-based problems. The CBSE Class 9 Angle Subtended by the chord explains concepts related to Equal chords of a circle subtending equal angles at the centre. CBSE Class 9 Perpendicular from centre to chord discusses the perpendicular from the centre of a circle bisects the chord. CBSE Class 9 Properties of Equal Chords explains that the perpendicular distance is the shortest line distance from a point. CBSE Class 9 Cyclic Quadrilaterals describe the relation between angles subtended by an arc at the centre and any point on the circle.

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#### Introduction to Circles

Circle is a closed figure on which every point is at a constant distance from a fixed point.

Chord is a line segment joining any two points on the circle and divides the circle into two parts, each part is called segment.

A continuous piece of a circle is called an Arc of the circle. The region between an arc and the two radii joining the centre to the end points of the arc is called a sector.#### Angle Subtended by The Chord

Equal chords of a circle subtend equal angles at the centre.

If two chords of a circle subtend equal angles at the centre, then the chords are equal.

These properties are valid in congruent circles also.

Angle subtended by a chord at the centre is double the angle subtended by it at any point on the circumference.#### Perpendicular From Centre to Chord

Perpendicular from centre of a circle bisects the chord.

Line segment joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.

The perpendicular bisectors of two chords of a circle intersect at its centre.

There is one and only one circle which passes through 3 non-collinear points.#### Properties of Equal Chords

Perpendicular distance is the shortest distance of the line from a point.

Equal chords are equidistant from the centre.

Chords that are equidistant from the centre are equal in length.#### Cyclic Quadrilaterals

Relation between angle subtended by an arc at centre and at any point on the circumference. Angles in same segment. Properties of cyclic quadrilaterals.

## CBSE Class 9 Textbook Solutions, Videos, Sample Papers & More

Students are recommended to practice and revise from the CBSE Class 9 Most important questions on Circles. The MCQs present in the CBSE Class 9 Multiple Choice Questions helps practice the problems that provide a competitive edge for future exams like NTSE, Olympiad, and more. CBSE Class 9 Short Answer section exposes an out-of-school ecosystem of questions that helps prepare for future competitive and board exams. Practising Short answer type questions by writing also improves thinking and problem-solving abilities.

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## CBSE Class 9 Frequently Asked Questions

NCERT Solutions for Class 9 Maths Chapter 10 is on Circles and is a crucial chapter as prescribed in the Class 9 syllabus by NCERT. The chapter Circle of Class 9 Maths includes an introduction to circles, the angle subtended by the chord, perpendicular from centre to chord, properties of equal chords and cyclic quadrilateral. There are five exercises in the Class 9 Maths Chapter 10 on circles. Apart from the NCERT Solutions drafted by experienced and qualified experts, students are recommended to go through the Sample papers, chapter notes, and question bank of the chapter, Circle.

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We should always follow a national curricular or framework drafted by eminent experts and follow NCERT Solutions for Class 9 Maths Chapter 10. The type of questions included across the five exercises of the chapter provides good exposure and experience to deal with different types of questions that can be asked in the school exams. Practising from NCERT Solutions for Class 9 Maths Chapter 10 will enable students to practice and attempt similar questions that may be asked in various exams. Once students are clear on the conceptual part and aware of the pattern of problems asked from a specific chapter, it becomes handy to tackle challenging problems based on that concept. It is also evident that a new typology of questions is included in the examinations like Case-based questions.

Students can get any time access to NCERT Solutions for Class 9 Maths Chapter 10, Circles on the TopperLearning website, where they can practice all the five exercises. Eminent and qualified experts carefully draft the solutions to these problems.

To understand Circles, a student must know about chords, diameter, radius, bisector and much more. The chapter Circle of Class 9 Maths includes an introduction to circles, the angle subtended by the chord, perpendicular from centre to chord, properties of equal chords and cyclic quadrilateral. There are five exercises in the Class 9 Maths Chapter 10 on circles, giving students an idea of different types of question patterns required to handle any questions in the exam.

To solve the problems of Class 9 Maths Chapter 10 Circles, one must understand the concepts first. With TopperLearning resources like the concept and problem-solving application videos, chapter-wise notes and question banks, students can clarify the concepts and then try to solve the NCERT solution independently.

The critical theorems of Class 9 Chapter 10 Circles are listed below.

- Theorem: Equal chords of a circle subtend equal angles at the centre.
- Theorem: This is the converse of the previous theorem. It implies that if two chords subtend equal angles at the centre, they are equal.
- Theorem: Equal chords of a circle are equidistant from the centre of a circle.
- Theorem: This is the converse of the previous theorem. It states that chords equidistant from the circle's centre are equal in length.
- Angle subtended by an arc at the centre of a circle is double that of an angle that arc subtends at any given point on the circle.
- Theorem: Angles formed in the same circle segment are always equal in measure.

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