CBSE Class 9 Maths Notes Chapter 10 Solutions PDF
Neha Tanna11 Sept, 2025
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CBSE Class 9 Maths Notes Chapter 10 Circles provide a complete overview to understanding circles, one of the most important topics in Class 9 Maths. These notes include clear explanations of concepts like chords, diameters, arcs, sectors, and concentric circles, along with important theorems and key formulas.
Students can use these notes for quick revision, better conceptual clarity, and effective exam preparation. Along with the solutions, we have included Cbse class 9 maths notes chapter 10 solutions, Ch 10 Maths Class 9 PDF Solutions, and Circles Class 9 Notes PDF to make learning easier and faster. Students can also refer to CBSE class 9 ncert solutions,CBSE class 9 syllabus, and CBSE class 9 sample papers for additional practice.
Introduction to Circle
A circle is one of the most important topics in Class 9 maths, covering concepts such as chords, tangents, arcs, sectors, and various theorems that help in solving problems efficiently. Understanding these basics lays a strong foundation for Class 10 maths. Using CBSE class 9 maths ncert solutions alongside these notes can further enhance preparation and clarity.
A circle divides a plane into three sections: the circle itself, the inside, and the outside. A chord is a line connecting two points on the circumference, and a chord passing through the centre is called a diameter. The circumference represents the perimeter of the circle. Equal-length chords subtend equal angles at the centre, and chords equidistant from the centre are equal.
In a cyclic quadrilateral, opposite angles sum to 180 degrees, and equal arcs correspond to equal chords. Using cbse class 9 maths ncert solutions, cbse class 9 syllabus, and cbse class 9 sample papers helps students practice and strengthen understanding.
CBSE Class 9 Maths Notes Chapter 10
The CBSE Class 9 Maths Notes Chapter 10 cover all key circle concepts, including chords, diameters, arcs, sectors, and important theorems. These notes help students revise quickly, understand formulas, and solve problems easily. Available in Cbse class 9 maths notes chapter 10 solutions, Ch 10 Maths Class 9 PDF Solutions, and Circles Class 9 Notes PDF.
- The circle splits a plane into three sections: the circle itself, the inside and outside of the circle.
- A chord is a line that travels around the circumference of a circle, connecting two points.
- A chord that goes through the centre is called a diameter.
- The circumference is the length of a circle's perimeter.
- Equal-length chords subtend equal angles at the middle. Likewise, if the chords' center-subtended angles are equal, then the chords are equal.
- A chord is divided in half by the perpendicular drawn on it from the centre. In the same way, if the line is drawn from the chord's centre to its bisect, it is perpendicular.
- Three non-collinear locations can only be traversed by one circle.
- Equally sized chords are spaced equally apart from the middle. Likewise, if two chords are equally spaced from the centre, they are equal.
- The sum of two angles that are opposite to one another in a cyclic quadrilateral is 180 degrees.
- The angles that the same line segment subtends are equal.
- The matching arcs will be congruent if the circle's chords have the same length. Similarly, matching chords will be equivalent if arcs are congruent.
CBSE Class 9 Maths Notes Chapter 10 PDF
The CBSE Class 9 Maths Notes Chapter 10 PDF is an excellent tool for learners who wish to develop strong reasoning and problem-solving skills. It gives students a lot of solved and unresolved problems together with a clear and short explanation of the ideas.
Students can download Cbse class 9 maths notes chapter 10 solutions, Ch 10 Maths Class 9 PDF Solutions, and Circles Class 9 Notes PDF to revise before exams. Along with these notes, references to cbse class 9 maths ncert solutions, cbse class 9 syllabus, and cbse class 9 sample papers are included to support practice and exam preparation:
CBSE Class 9 Maths Notes Chapter 10 Solutions
The CBSE Class 9 Maths Notes Chapter 10 Solutions cover important circle concepts like chords, diameters, arcs, sectors, and concentric circles with clear definitions, examples, and diagrams. Key theorems, such as perpendiculars bisecting chords and equal chords being equidistant, are explained concisely.
Using these notes along with Ch 10 Maths Class 9 PDF Solutions and Circles Class 9 Notes PDF helps students revise quickly and prepare effectively. Students can also refer to cbse class 9 maths ncert solutions, cbse class 9 syllabus, and cbse class 9 sample papers for extra practice.
Circle
The locus of the points at a certain distance from a fixed point is defined as a circle.
Chord
A chord is a straight line that connects any two points on a circle.
Circumference
A circle's circumference is its entire length. A circle's perimeter, also known as its border curve, is its circumference.
Arc
Any segment or portion of the circumference is an arc. A circle is divided into two equal parts by its diameter. Anything smaller than a semicircle is called a minor arc. Any arc greater than a semicircle is considered a major arc.
Sector
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A sector is the area between an arc and the two radii that connect the arc's centre and endpoints.
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A segment is a section of a circle that has been cut off by a chord.
Concentric Circles
Concentric circles are circles with the same centre.
Theorem 1
A straight line drawn from the centre of a circle to bisect a chord which is not a diameter, is at right angles to the chord.
Theorem 2
(Converse of theorem 1)
The perpendicular to a chord from the centre of a circle bisects the chord.
Theorem 3
Equal chords of a circle are equidistant from the centre.
Theorem 4
(Converse of theorem 3)
Chords which are equidistant from the centre of a circle are equal.
Theorem 5
There is one circle, and only one, which passes through three given points not in a straight line.
Theorem 6
The angle at which an arc of a circle subtends at the centre is double the angle at which it subtends at any point on the remaining part of the circumference.
Theorem 7
Angles in the same segment of a circle are equal.
Theorem 16
If two chords of a circle intersect externally, then the product of the lengths of the segments are equal.
Theorem 17
If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square on the length of the tangent from the point of contact to the point of intersection.
CBSE Class 9 Maths Notes Chapter 10 Circles PDF Download
Here, we have provided CBSE Class 9 Maths Notes Chapter 10. Students can view these CBSE Class 9 Maths Notes Chapter 10 before exams for better understanding of the chapter.
CBSE Class 9 Maths Notes Chapter 10: Maths has never been easy because many people find it quite difficult to memorize the formulas. However, our class 9 Maths Chapter circle notes help you quickly recall everything. Our notes are made under the most recent CBSE curriculum, which makes it easier and faster for you to learn the topics.
Additionally, the CBSE Class 9 Maths Notes Chapter 10 Circles download option makes studying offline easier. Therefore, we have you covered if you need to learn topics rapidly or if you need practical formulas while learning.
CBSE Class 9 Maths Notes Chapter 10 PDF Download
Benefits of CBSE Class 9 Maths Notes Chapter 10
Using Cbse class 9 maths notes chapter 10 solutions, Ch 10 Maths Class 9 PDF Solutions, and Circles Class 9 Notes PDF, students can revise quickly, strengthen concepts, and prepare effectively for exams.These notes provide a structured approach to learning, help in problem-solving, and serve as a reliable reference alongside cbse class 9 maths ncert solutions, cbse class 9 syllabus, and cbse class 9 sample papers
CBSE Class 9 Maths Notes Chapter 10 FAQs
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