by Tiwari Academy
NCERT Solutions for Class 9 Maths Chapter 9 Circles in English and Hindi Medium updated for new session 2025-26. According to revised syllabus and new NCERT books for CBSE 2025-26, there are only three exercises in chapter 9 of 9th Maths. Class 9 students often face challenges when it comes to mastering Chapter 9, Circles, in NCERT Mathematics Textbook. To ease this process, many rely on NCERT Book Solutions for Class 9 Mathematics Chapter 9 Circles, which provide step-by-step explanations for all questions. NCERT Class 9th Math Book Chapter 9 Notes are a great way to revise the key concepts and theorems covered in this chapter.
Class 9 Maths Chapter 9 Solutions: CBSE Board
These notes, combined with NCERT Textbook Class 9 Maths Topics Chapter 9 Exercises, enable students to strengthen their grasp on concepts like tangents and secants. Class 9 NCERT Maths Circles Important Questions help in practicing frequently asked questions, making the preparation more effective. For easy access, students can download the NCERT Mathematics Class 9 Chapter 9 Solutions PDF, which provides all solutions and Class 9 Math Chapter 9 Theorems in a structured format.
Class 9 Maths Exercise 9.1 in English
Class 9 Maths Exercise 9.2 in English
Class 9 Maths Exercise 9.3 in English
Preparing for exams becomes easier with a comprehensive understanding of NCERT Mathematics Chapter 9, Circles, in the CBSE syllabus. The Class 9 Maths Chapter 9 Solution PDF provides detailed solutions that clarify concepts and improve problem-solving skills. Students can also refer to the NCERT Class 9 Math Exercise Chapter 9 Study Material, which includes well-structured explanations for all exercises. For those looking for quick revision, the Class 9 Mathematics Book Chapter 9 Notes are highly useful.
Class 9 Maths Chapter 9 Solutions: State Boards
The NCERT Guide Class 9th Maths Chapter 9 Guide ensures that no important topic, like tangent properties, is missed. Practice is essential, and the Class 9 Maths Chapter 9 Practice Questions in the NCERT Simplified Class 9 Mathematics Textbook Solutions PDF allow students to refine their skills and build confidence. Worksheets and Class 9 Maths Chapter 9 Worksheets can further aid in self-assessment and preparation.
Class 9 Maths Chapter 9 Exercise 9.1
Class 9 Maths Chapter 9 Exercise 9.2
Class 9 Maths Chapter 9 Exercise 9.3
Class 9 Maths Chapter 9 Exercise 9.4
NCERT Solutions for Class 9 Maths Chapter 9
To achieve excellent results in the Circles chapter, students should focus on practicing with resources like the NCERT Class 9 Mathematics Chapter 9 PDF. These solutions cover all exercises, including Class 9 NCERT Maths Circles Exercise Solutions, ensuring comprehensive preparation. NCERT Class 9th Math Chapter 9 Problems from previous exams are included in the NCERT Textbook 9th Mathematics Chapter 9 Answers, helping students understand the exam pattern. To enhance preparation, students can explore Grade 9th NCERT Maths Circles Chapter 9 Solutions, which break down each concept into simpler steps.
Class 9 Maths Chapter 9 Solutions: Hindi Medium
Revisiting the Class 9 Math Topics Chapter 9 Theorems and practicing NCERT Detailed Solutions Chapter 9 Circles solidifies core concepts. The Class 9 Maths Circles Important Questions highlight topics likely to appear in exams, making these solutions a one-stop destination for success in NCERT Class 9 Maths Chapter 9 Circles. Tiwari Academy’s solutions can serve as valuable revision tools. Students can revisit specific topics or problem-solving techniques when preparing for exams, helping them consolidate their knowledge.
Class 9 Maths Exercise 9.1 in Hindi
Class 9 Maths Exercise 9.2 in Hindi
Class 9 Maths Exercise 9.3 in Hindi
| Class: 9 | Mathematics |
| Chapter 9: | Circles |
| Number of Exercises: | 3 (Three) |
| Content: | NCERT Exercises Solution |
| Mode of Content: | Images, PDF, Text and Videos Format |
| Academic Session: | CBSE 2025-26 |
| Medium: | Hindi and English Medium |
Important Points in Class 9 Maths Chapter 9 for Annual Exams
Circle and Related Terms: Definitions of circle, radius, diameter and chord.
Tangent to a Circle: Properties of tangents, especially the perpendicularity of the tangent at the point of contact.
Theorems: Key theorems on tangents, including equal tangents from an external point.
Construction Problems: Practical geometry involving tangents.
Application of Properties: Solving problems using tangent properties and theorems.
| Day | Topics to Cover | Resources | Practice Work |
|---|---|---|---|
| Day 1 | Introduction to Circles and Basic Terms | NCERT textbook, Class 9 Maths Chapter 9 Notes | Revise definitions and solve 5 basic questions. |
| Day 2 | Properties of Tangents | NCERT Solutions for Chapter 9, Online Videos | Solve all exercise problems related to tangent properties. |
| Day 3 | Theorems on Tangents | Class 9 Maths Circles Chapter Solutions | Write and learn the proofs of key theorems, practice 5 examples. |
| Day 4 | Solving Complex Problems | NCERT Class 9 Maths Chapter 9 Solutions PDF | Solve additional questions from reference books or guides. |
| Day 5 | Construction Problems | Class 9 Maths Chapter 9 Notes, Geometry Tools | Practice 3-4 construction problems step by step. |
| Day 6 | Revision and Doubt Clearing | Class 9 Maths Chapter 9 Worksheets | Review important points, clarify doubts and attempt mock tests. |
| Day 7 | Full Chapter Test | Mock Test Papers | Attempt a timed test to evaluate your preparation. |
UP Board NCERT Solutions for Class 9 Maths Chapter 9 Prashnavali 9.1, Prashnavali 9.2 and Prashnavali 9.3 in Hindi Medium to study online or download in PDF format free for the new CBSE session 2025-26. All the solutions for 9th Maths are updated for the new session based on NCERT (https://ncert.nic.in/) Books 2025-26. Most of the state board like UP Board, MP Board, Jammu and Kashmir, Uttarakhand, etc., are now following NCERT Textbooks for their academic session. So, these solutions are applicable for all these boards also. All the questions are explained well using the theorems of circles and giving proper examples. In few questions some axioms of circles are also used as theorems.
Class 9 Maths Study Material for Chapter 9
Class 9 Maths Chapter 9 Practice Questions with Solution
What do understand by a circle?
Circle: A circle is the collection of all points in a plane, which are at a fixed distance from a fixed point in the plane.
What are the components of a circle?
1. Diameter: It is the longest chord of the circle.
2. Circumference: The length of complete circle is called its circumference.
3. Arc: A piece of circle between two point is called arc.
4. Segment: The region between a chord and either of its arcs is called a segment of circular region.
Properties related to CIRCLE
1. Equal chords of a circle subtend equal angles at the centre.
2. If the angles subtended by two chords of a circle at the centre are equal, the chords are also equal.
3. The perpendicular from the centre of a circle to a chord bisects the chord.
4. The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
5. There is one and only one circle passing through three non-collinear points.
NCERT Textbook Solutions and CBSE Offline Apps of other subjects are also available free to use or download. Solutions are prepared for CBSE and UP Board students appearing in 2025-26 CBSE Exams and following the updated NCERT Books. UP Board NCERT Solutions for Class 9 Maths Chapter 9 Circles all Exercises are given below.
Important Questions on 9th Maths Chapter 9
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
AC is diameter of circle. Hence, ∠ADC = 90° and ∠ABC = 90° … (1) [∵ Angle in a semicircle is a right angle.] Similarly, BD is diameter of circle. Hence, ∠BAD = 90° and ∠BCD = 90° … (2) [∵ Angle in a semicircle is a right angle.] From the equation (1) and (2), ∠ADC =∠ABC = ∠BAD = ∠BCD = 90° Hence, ABCD is a rectangle.
Fill in the blank: The centre of a circle lies in _____________ of the circle.
The centre of a circle lies in interior of the circle.
A circle has only finite number of equal chords. True or False?
False. Because, there are infinite number of equal chords in a circle.
Sector is the region between the chord and its corresponding arc. Is it true or false?
Sector is the region between the chord and its corresponding arc. False. Because, between chord and arc a segment is formed. Sector is the region which is formed between radii and arc.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Given: Triangle ABC and ADC are two right triangle on common base AC.
To prove: ∠CAD = ∠CBD.
Proof: Triangle ABC and ADC are on common base BC and ∠BAC = ∠BDC.
Hence, points A, B, C and D lie on the same circle.
[∵ 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.]
Therefore, ∠CAD = ∠CBD [∵ Angles in the same segments are equal]
Important Theorems on Circles Class 9 Mathematics Chapter 9
1. Equal chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal.
2. If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs are congruent.
3. Congruent arcs of a circle subtend equal angles at the centre.
4. 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.
Need of NCERT Solutions for Class 9 Maths Chapter 9 Circles
NCERT Exercise Solutions for Class 9 Maths Chapter 9 Circles provide comprehensive answers and step-by-step explanations to all the exercises in this chapter. These solutions cover important concepts, including Class 9 Mathematics Circles Theorems and properties of tangents and secants. They also include Class 9 Math Circles Chapter Solutions for every question, helping students strengthen their understanding. The Class 9 Maths Chapter 9 PDF can be downloaded for easy access, offering detailed explanations. With these solutions, students can efficiently prepare for exams and gain confidence by solving Class 9 Mathematics Textbook Circles Exercise Solutions, along with additional Class 9 Maths Chapter 9 Problems for practice.
Importance of Class 9 Maths Chapter 9 Notes
NCERT Class 9 Mathematics Chapter 9 Notes summarize the key points and theorems of the chapter on Circles, making revision quicker and easier. These notes highlight important Class 9 Maths Circles Important Questions and are an excellent resource for last-minute exam preparation. They complement the NCERT Class 9 Math Chapter 9 Solutions PDF, ensuring students can revise concepts systematically. By using these notes along with NCERT Mathematics Solutions Chapter 9 Circles, students can reinforce their learning. The Class 9 Maths Chapter 9 Notes act as a concise guide that helps retain core concepts, including properties of tangents, which are crucial for scoring well in exams.
5. Angles in the same segment of a circle are equal.
6. Angle in a semi-circle is a right angle.
7. The sum of either pair of opposite angles of a cyclic quadrilateral is 180 and if the sum of a pair of opposite angles of a quadrilateral is 180, then the quadrilateral is cyclic.
How can I prepare better for Class 9 Maths Chapter 9 Circles?
To prepare effectively for NCERT 9th Mathematics Chapter 9 Circles, students should first understand the fundamental concepts provided in the Class 9 Maths Chapter 9 Notes. Using resources like the NCERT Class 9 Maths Chapter 9 PDF, students can practice Class 9 Math Chapter 9 Practice Questions and solve all the exercises. The Class 9 Maths Circles Chapter Solutions are particularly helpful for clearing doubts and refining problem-solving skills. Revising Class 9 Mathematics Chapter 9 Theorems regularly ensures a solid grasp of the chapter. Downloading the NCERT Class 9 Maths Solutions PDF provides access to comprehensive materials and ensures thorough exam preparation.
What are Class 9 Maths Circles Important Questions?
Class 9 Maths Circles Important Questions are a curated set of questions that focus on the key concepts and theorems of Chapter 9. These questions are highly likely to appear in exams and serve as excellent practice material. They are included in the NCERT Class 9 Maths Chapter 9 Guide to ensure students focus on critical areas such as tangent properties and their applications. Paired with the Class 9 Maths Chapter 9 Practice Questions, they help students identify their strengths and weaknesses. By solving these and revisiting Class 9 Maths Circles Exercise Solutions, students can achieve better clarity and confidence for exams.
Where can I find Class 9 Maths Chapter 9 Worksheets?
NCERT Class 9 Maths Chapter 9 Worksheets can be found in various online resources and are often included in the NCERT Class 9 Maths Chapter 9 Study Material. These worksheets are designed to provide additional practice, focusing on Class 9 Maths Circles Important Questions and Class 9 Maths Chapter 9 Problems. They often include a mix of theoretical and practical questions, allowing students to test their understanding of key concepts like tangents and secants. These worksheets complement the Class 9 Maths Circles Chapter Solutions, helping students revise efficiently. Downloading the NCERT Class 9 Maths Chapter 9 Solutions PDF often includes such worksheets for practice.
