NCERT Solutions For Class 9 Maths Chapter 10 Circles (Ex 10.2) Exercise 10.2
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Mathematics is a field that is concerned with the study of numbers, their relations, formulas, quantities, analysis, space and shapes. The study of Mathematics is an integral part of Engineering, Science, Medicine, Accounting and Finance, Computer Science, etc. Mathematics lays the foundation for a lot of careers in the field of Engineering, Flying, Statistics, Insurance, and many more. Mathematics helps in developing several skills that are crucial to the overall development of an individual. It helps develop skills like critical thinking, problemsolving, logical reasoning, quantitative aptitude, time management and analysis, etc. Acquiring these skills can help in clearing many competitive examinations that students appear for like NEET, JEE Mains, JEE Advance, AIIMS, CAT, CUET, etc. Students must inculcate these skills in them to be able to perform well in the concerned examinations.
Developing these skills can help students in paving the path for their careers in various fields, hence students must study Mathematics with utmost sincerity. Having a thorough and correct knowledge of mathematical concepts is important for students to be able to establish a successful career. Students of Class 9 can refer to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 to strengthen their basic mathematical knowledge. It is advisable for students of Class 9 to take the help of the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 to score good marks in the senior secondary examination. Students can access the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 from the Extramarks website.
NCERT Solutions For Class 9 Maths Chapter 10 Circles (Ex 10.2) Exercise 10.2
Extramarks is a renowned educational website. A wide range of study materials and learning resources can be availed by students from the Extramarks website. Extramarks caters to the academic needs of students and equips them with the required educational material. Students of all classes can obtain the needed study material from the Extramarks website or mobile application. Extramarks provides a range of educational resources from NCERT solutions, sample papers, past years’ papers, online live sessions, revision notes, mock tests, etc. Students may sometimes be unable to access online study material due to a lack of access to the internet, keeping in mind the requirement of every student, Extramarks also provides downloadable pedagogical resources on the Extramarks website or mobile application.
A downloadable PDF file of NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 is also available for students of Class 9 who may have internet connection issues or who would prefer to refer to downloaded files. Students who prefer to study from hardcopy study material can access the downloadable PDF files and get them printed. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 are one of the most reliable and wellexplained answers that students of Class 9 can refer to for their preparation. Students of Class 9 may download the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 in PDF format from the Extramarks website if they require offline access.
Access NCERT Answers for Class 9 Mathematics Chapter 10 – Circles
Students appearing for the Senior Secondary Examination must make it a point to go through their syllabus properly and thoroughly to be able to secure the highest marks possible. Students must understand the significance of performing well in the senior secondary examination. The marks that students secure in the senior secondary examination help set the tone for their academic progression. The Class 9 Maths Chapter 10 Exercise 10.2 is one of the most significant exercises that are covered in the syllabus of the NCERT Mathematics Chapter 9 Circles. Circles can be a complicated topic, students must understand the concepts that have been covered in this chapter and practice them well. Students may utilise the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 for their preparation for the senior secondary examination.
The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 have been elaborated extensively for better comprehension for students. Students can refer to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 and practice solving the questions that are a part of Exercise 10.2 Class 9 Maths for better preparation. Students appearing for the Senior Secondary Examination of Mathematics are supposed to prepare for the concerned examination beforehand. Starting the preparation for the senior secondary examination well in advance can help give an edge to students’ preparation. It may improve the chances of scoring higher marks in the exams.
NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.2
The Class 9 Maths Chapter 10.2 Circles is one of the most important chapters covered in the NCERT curriculum of Mathematics. Circles are a topic that can be quite technical. Students are not only required to understand the concepts to be able to master this chapter but they should be able to get a good grasp of how to apply those concepts practically. Students are encouraged to practice the Maths Ex 10.2 Class 9 to have a better understanding of the practical applications required in Chapter 10 Circles. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 can prove to be of great assistance to students in their preparation for the Senior Secondary Examination of Mathematics.
Students are suggested to regularly practice the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 to have a good grasp of the technical and applicationbased concepts introduced in the Chapter Circles. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 can be accessed by students from the Extramarks website or mobile application. Students are required to register themselves on the Extramarks website to be able to access the pedagogical material they require. Once registered on the Extramarks website, students can access any study material they require from sample papers, practice papers, past years’ papers, revision notes, online live sessions, doubtclearing sessions, NCERT solutions, mock tests, etc.
NCERT Solutions for Class 9
The NCERT curriculum is prepared following the CBSE board guidelines. Students who are registered under the CBSE board are recommended to study from the NCERT textbooks. Students should get prepared for their senior secondary examination with the help of the NCERT exercise problems and solutions. Students of Class 9 may make use of the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 to prepare for the examination of Mathematics. NCERT solutions to all exercise problems of all subjects are available on the Extramarks website and mobile application. Students of Class 9 can access the necessary study material and NCERT Solutions for all subjects as per their requirements from the Extramarks website and learning application.
To secure high marks in the senior secondary examination, students must go through the NCERT textbook thoroughly. Students are suggested to start going through the concerned syllabus from the beginning of the academic course of the NCERT textbook. Starting the preparation early can give students the upper hand they require to ace the senior secondary examination. Students who have trouble understanding the concepts covered in Chapter 10 of the NCERT textbook of Mathematics may take help from the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 available on Extramarks. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 provided by Extramarks have been curated by professionals of the concerned field for the best result possible for students.
CBSE Study Materials for Class 9
Students of Class 9 can access the study material based on the CBSE board guidelines from the Extramarks website. While preparing for the senior secondary examination, students must refer to the study material that has been prepared following the CBSE board guidelines. The study material and learning resources provided by Extramarks have been designed in a manner that applies to the CBSE board guidelines. Students who have to prepare for the Senior Secondary Examination of Mathematics can refer to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 from the Extramarks website and learning application.
The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 can be used by students as a tool to enhance their preparation process. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 availed by Extramarks have been designed elaborately. They have been explained for students to have a better understanding of the breakdown of steps to solve the exercise problems efficiently. Students are advised to be sincere with their preparation for the senior secondary examination as the grades secured by students in the senior secondary examination can influence the career path they choose to take. Students are encouraged to refer to past years’ papers from time to time, to be familiar with the question paper pattern. Being familiar with the question paper pattern can help students gain confidence about examination questions.
CBSE Study Materials
The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 have been designed by experts based on the latest syllabus of the Central Board of Secondary Education. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 come highly recommended for the preparation of the senior secondary examinations administered by the Central Board of Secondary Education. Extramarks also provides downloadable revision notes for students to keep revising the syllabus that they have already studied thoroughly. Students who have thoroughly covered the syllabus of Class 9 Chapter 10 Circles and practised the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 are recommended to go through the revision notes of the concerned syllabus.
Students must prepare themselves for the Senior Secondary Examination of Mathematics with utmost sincerity. The senior secondary examination of Class 9 is one of the most important examinations that students take in their academic careers. The NCERT Mathematics Chapter 10 Circles is one of the most technical and practical chapters. Due to its applicationbased nature, knowing the concepts introduced in the concerned chapter is not enough, students must also consistently practice the exercise solutions to master the technical skills required for an overall understanding of the said chapter. To perform well in the senior secondary examination, students are required to thoroughly cover the concerned syllabus. Students can access the necessary learning resources from the Extramarks website and mobile application.
Q.1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Ans
$\begin{array}{l}\text{Given}:\text{Two congruent circles with centre O and O\u2019 i}\text{.e}\text{., OA}=\text{OP,}\\ \text{OB}=\text{O\u2019Q and}\angle AOB=\angle PO\u2018Q\text{.}\\ \text{To prove: chord AB}=\text{chord PQ}\\ \text{Proof}:\text{In}\Delta AOB\text{and}\Delta PO\u2018Q\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}OA=O\u2018P\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\text{Radii of congruent circles}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\angle AOB=\angle PO\u2018Q\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\text{Given}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}OB=O\u2018Q\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\text{Radi}i\text{of congruent circles}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\therefore \Delta AOB\cong \Delta PO\u2018Q\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[By\text{S}\text{.A}\text{.S}\text{.}\right]\\ \text{Therefore,}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}AB=PQ\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[By\text{C}\text{.P}\text{.C}\text{.T}\text{.}\right]\\ \text{Thus},\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{chord AB}=chord\text{PQ}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}\hspace{0.17em}Hence proved}\text{.}\end{array}$
Q.2 Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Ans
$\begin{array}{l}\text{Given}:\text{Two congruent circles with centre O and O\u2019 i}\text{.e}\text{., OA}=\text{O\u2019P,}\\ \text{OB}=\text{O\u2019Q and}\angle AOB=\angle PO\u2018Q\text{.}\\ \text{To prove: chord AB}=\text{chord PQ}\\ \text{Proof}:\text{In}\Delta AOB\text{and}\Delta PO\u2018Q\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\text{\hspace{0.17em}}OA=O\u2018P\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}[Radii of congruent circles]}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\angle AOB=\angle PO\u2018Q\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\mathrm{Given}\right]\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}\mathrm{OB}=\mathrm{O}\u2018\mathrm{Q}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}\hspace{0.17em}[\mathrm{Radii}\mathrm{of}\mathrm{congruent}\mathrm{circles}]\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}\therefore \mathrm{\Delta AOB}\cong \mathrm{\Delta PO}\u2018\mathrm{Q}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\hspace{0.17em}}[\mathrm{By}\mathrm{S}.\mathrm{A}.\mathrm{S}\mathrm{.}]\\ \text{Therefore},\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}AB=PQ\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[By\text{C}\text{.P}\text{.C}\text{.T}\text{.}\right]\\ \text{Thus},\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{chord AB}=\mathrm{chord}\text{PQ}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Hence proved}\text{.}\end{array}$
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FAQs (Frequently Asked Questions)
1. How important is the Chapter 10 Circles of Class 9 Mathematics syllabus?
Chapter 10 Circles is an important part of the syllabus of Mathematics syllabus of Class 9. Students must understand the significance of this chapter in the Senior Secondary Examination of Mathematics. Chapter 10 Circles has a high marks weightage in the senior secondary examination. Circles is a chapter that is highly technical and applicationbased, students are required to go through this chapter in detail. Since it is an applicationbased chapter, students must practice the NCERT exercise problems and solutions of this chapter regularly and repeatedly. For their preparation, students can make use of the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 which can be accessed from the Extramarks website
2. Is the Class 9 Senior Secondary Examination of Mathematics difficult?
The Class 9 Senior Secondary Examination of Mathematics can be a tough exam. However, it is not tough to score high marks in the senior secondary examination if students prepare thoroughly before appearing for the examination. To perform well in the Senior Secondary Examination of Mathematics, students must intensively cover the concerned syllabus. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.2 can be used by students for their preparation.