# NCERT Solutions Class 9 Maths Chapter 10

## NCERT Solutions For Class 9 Mathematics Chapter 10 – Circles

Mathematics is a subject that can be easily learned by students by regularly revising and practising a lot of questions and answers. Suppose you are willing to learn more about the nature and construction of different mathematical shapes. In that case, you must take full advantage of the class notes and question banks available on the Extramarks website for Class 9 Mathematics Chapter 10 – Circles.

A circle has been defined as a cumulation of all the points in a particular plane, such that all points located on the surface of this 2-dimensional shape are at a fixed distance from the centre.  According to the NCERT Solutions for Class 9 Mathematics Chapter 10, circles are categorised as having a fixed radius or distance between the surface and the centre and a fixed centre to satisfy the conditions of being this particular mathematical shape.

You can quickly look at the premium study material and detailed class notes on NCERT Solutions for Class 9 Mathematics Chapter 10 by visiting Extramarks’ website. It is considered to be the most renowned platform and is trusted by lakhs of students across India. The platform provides the students with the required skills and knowledge about the different topics covered in this chapter. On the Extramarks website, you will get high-quality study notes and solved examples to develop better conceptual clarity and a theoretical understanding of these mathematical formulas and concepts.

One can get access to the syllabus and quality study notes for the CBSE board for every subject through our Extramarks website. Once you register on our website, you can get access to different solved answers and questionnaires for NCERT Solutions Class 12, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 11, NCERT Solutions Class 6, and so on.

## Key Topics Covered In NCERT Solution For Class 9 Mathematics Chapter 10 – Circles

The important topics explained in this chapter include Chords of a Circle, Circle through 3 Points, Arc of a Circle, Angles subtended within a Circle by Chords and Arcs, Cyclic Quadrilaterals, and Optional exercises.

The key topics and essential exercises included in our Class 9 Mathematics NCERT Solutions Chapter 10 – Circles are listed below:

• Introduction
• Chords and Arcs of a Circle
• Circle through 3 Points in Space
• Angles subtended within a Circle by Chords and Arcs

Students will get step-by-step instructions and explanations around each of these topics in our NCERT Solutions for Class 9 Mathematics Chapter 10.

Introduction

A circle has many components, which can be defined as follows –

Radius – is the distance between the centre of the circle and any of the points located on the planar surface (also known as the circumference) of a circle.

Diameter –  is the perpendicular distance between any two points located on the opposite ends of the surface of a circle, which also passes through the centre of the circle.

Tangent – It is a line directly touching the surface of a circle at a perpendicular point within the shape’s exterior. It is parallel to the radius and diameter of the circle at the same time.

Segment – It is the area enclosed by the chords of a circle while being separated by the centre of the circle.

Sector – It is the area enclosed by the arcs of a circle while being at a fixed distance from the centre of the circle.

Chords And Arcs Of A Circle

1. Chord – It is the average distance between any two points within the surface of a circle, given that the line segment joining these two points doesn’t pass through the centre of the circle.
2. Arc – An arc is defined as the portion of the area enclosed by any two points within the surface of a circle, given that the lines joining them subtend an acute angle from the centre of the circle. The two types of arcs namely, Minor Arc and Major Arc depend upon the value of the angle subtended by the line segments joining the respective points with the Centre of the Circle.

We want one beginning stage and one completion point to define a straight boundary. That implies a line needs two points to be drawn. Likewise, if we should draw a circle, we want to have a few focuses. However, unlike line fragments, we have various ways of drawing a circle. If a circle can be drawn with a single point because it does not have many planes, the starting point will also become the ending point.

Essentially, we can draw a circle using two focuses. We can draw a few circles from two different points, just like we did from a single point. Be that as it may, the ongoing errand is to draw a circle going through three focuses located at the circle’s centre. While considering a circle going through three focuses, noticing two cases is significant. Since the focuses might be either collinear or non-collinear, the circle might go through collinear focuses or non-collinear points on the circle.

Angles Subtended Within A Circle By Chords And Arcs

We will examine the hypothesis connected with the point subtended by an arc of a circle and its confirmation with complete clarification. The point subtended by an arc in the middle is twofold. the point occupied by it at any time on the circle’s leftover pieceIf the harmonies of the two circles are equivalent, and the arcs that connect them are also harmonious. On the other hand, if two arcs are compatible, their contrasting harmonies are equivalent. The point subtended by an arc in the middle is twofold. It can occupy any point on the excess piece of the circle. A line portion joining two focuses subtends equivalent points at two different focuses lying on a similar side of the line containing the line fragment; the four focuses lie on a circle.

A quadrilateral named WXYZ is called cyclic if all four vertices lie on a circle. The amount of one or the other set of inverse points of a cyclic quadrilateral is 180º. The Circle can have an infinite number of harmonies. In the figure given, we see that the more drawn-out harmony is closer to the middle than the more subtle harmony. The breadth is the longest harmony from the middle; the distance is zero since the middle lies on it. On the off chance that the angle between a couple of inverse points of a quadrilateral is 180º, the quadrilateral is cyclic.

NCERT Solutions for Class 9 Mathematics Chapter 10 – Exercise & Solutions

NCERT solutions for Class 9 Mathematics Chapter 10 have detailed answers to the textbook exercises, solved examples, and additional questions for practice. You can level up your preparation and improve your performance in the examinations by referring to it.

Our Mathematics subject matter experts have given the solutions. All the solutions are in a step-by-step format, including every single point required while calculating every answer. Experienced teachers from the field of Mathematics have curated the solutions given in the study materials. Hence, you can wholeheartedly trust our study resources.

Click on the below links to view exercise-specific questions and solutions for NCERT Solutions for Class 9 Mathematics Chapter 10:

• Chapter 10: Exercises and Solutions

Along with Class 9 Mathematics solutions, you can explore NCERT Solutions on our Extramarks’ website for all primary and secondary classes

• NCERT Solutions Class 1
• NCERT Solutions Class 2
• NCERT Solutions Class 3
• NCERT Solutions Class 4
• NCERT Solutions Class 5
• NCERT Solutions Class 6
• NCERT Solutions Class 7
• NCERT Solutions Class 8
• NCERT Solutions Class 9
• NCERT Solutions Class 10
• NCERT Solutions Class 11
• NCERT Solutions Class 12

NCERT Exemplar Class 9 Mathematics

The NCERT Exemplar Class 9 Mathematics book covers complex theories that guide the students in preparing for and facing the upcoming examinations confidently. This book assists students in developing confidence during their preparation by providing basic and advanced-level questions. Students can refer to it for additional practice.

The questions are designed as per the pattern of the CBSE as well as competitive examinations. This will aid students in solving all types of questions with accuracy, helping them develop an interest in the subject at large. Our solutions have always proven to be a remarkable guide for the students preparing for their school examinations and other competitive examinations like NEET, JEE, WBJEE, BITSAT, MHT-CET etc.

Students can ensure guaranteed success once they include NCERT solutions for Class 9 Mathematics Chapter 10 and NCERT Exemplar Class 9 Mathematics in their study material. Both of these resources can be easily accessed from the Extramarks’ website.

Key Features for NCERT Solutions for Class 9 Mathematics Chapter 10

To score well, you must revise the concepts repeatedly. Hence, NCERT Solutions for Class 9 Mathematics Chapter 10 offers guides to revise appropriately. The key features are as follows:

• The revision-related material can be accessed from our NCERT Solutions Class 9 Mathematics Chapter 10.
• It has concepts divided into various segments, helping students get an in-depth understanding of the chapters.
• NCERT Solutions for Class 9 Mathematics Chapter 10 provides well-explained solutions to all the questions in the textbook and provides sample question papers to be thorough in their respective subjects.
• The solutions provided by the Extramarks help students be confident, improve their learning abilities, understand those complex topics with ease, and prepare well for the examinations to get excellent results.

We recommend students sign up for NCERT Solutions for Class 9 Mathematics Chapter 10 on Extramarks’ website for a  detailed explanation of the Circles chapter.

## 1. What are the important points I should keep in mind while solving problems in mathematics?

Students should keep in mind the following important points while solving problems in Mathematics:

1. They must read each question carefully and attentively. Analyse the type of problem.
2. They must note down all the conditions given in the questions on a piece of paper.
3. They must solve it in a step-by-step format.
4. They must begin with easy steps and calculations.
5. They must double-check from the start once the calculation is done.

## 2. Are NCERT Solutions for Class 9 Mathematics Chapter 10 difficult?

The entire chapter is moderately complex chapter for students to understand, and many students may face problems as these lessons are graded. Rote learning may give you partial success, but not for long. Therefore, we humbly suggest you sign up at  NCERT Solutions for Class 9 Mathematics Chapter 10, which will definitely solve your problem to a great extent. These solutions are designed in such a way that the answers are self-explanatory, which means that students may not always have to rely on teachers to clear their doubts while studying, particularly during last-minute preparation, making it easier to understand the concepts quickly and thoroughly.