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NCERT Solutions for Class 10 Maths Chapter 10 – Circles

NCERT Solutions for Class 10 Maths Chapter 10-Circles are prepared by our subject matter experts. The solutions are in a step by step format for facilitating easy understanding and learning of the chapter. The important topics covered in this chapter are centre, radius, diameter, chord, the tangent of a circle, arc, sector, circumference and various theorems. The two important theorems covered in this chapter include “Number of tangents drawn from a given point” and “Tangent Perpendicular to the radius at the point of contact.”

Our NCERT Solutions have been prepared as per the current CBSE Class 10 Maths Syllabus. They are easy to understand, completely accurate and to the point. They abide by the updates given by the CBSE board and NCERT. This chapter comprises 2 comprehensive exercises that contain various types of question types such as MCQs, fill in the blanks, short answer questions, long answer questions, direct questions and application-based questions. Our NCERT Solutions for Class 10 Maths Chapter 10-Circles explicitly answer all questions of all the exercises.

Our Maths shortcuts and smart study strategies help you learn faster, better and score more marks in your board exams. They make the earning process a more natural, enjoyable and effective and happy process. Our NCERT Solutions keep your doubts cleared and conceptual base strong to aid you in not only scoring well in your Class 10 board exams but also help you do well in your Class 12 boards and various competitive exams. They have been specifically designed to help you improve your retention rate, overall speed and efficiency.

CBSE NCERT Class 10 Maths Chapter 10: Important Topics

Here, in NCERT Solutions for Class 10 Maths Chapter 10-Circles, you will be introduced to the concept of Circles. It covers all significant topics and sub-topics associated with circles. Some of them have been discussed below.

 

  • Introduction 

 

In NCERT Class 10 Maths Chapter 10 – Circles, you will be taught how all the points together make a figure at an equal distance from a fixed point. In this, you will be learning more about the below-mentioned points. 

 

  • Center

 

In this section, you will learn that a particular point in the middle of the circle will be called a centre. 

 

  • Radius

 

This part of NCERT Class 10 Maths Chapter 10 will teach you that a straight line from the centre of the circle to any point on the circle’s circumference is called a radius.

 

  • Chord

 

This part of the chapter will teach you that the line segment joining any two points on the circle’s circumference is called a Chord. 

 

  • Diameter

 

In CBSE NCERT Class 10 Maths Chapter 10, you will learn that The longest chord which passes through a circle is called the diameter. Diameter is also twice the radius.

Our NCERT Solutions for Class 10th Maths Chapter 10 – Circles, also teach you about circumference, arc, sector and segment. 

 

  • Tangent to a Circle

 

In this part of Maths Chapter 10 – Circles, you will be learning about a tangent. A line that touches or passes through a circle at only one point on its circumference is termed as a tangent to a circle. 

Here you will be reading in detail about it with the help of various diagrams. In Class 10 Maths Circles, you will learn about tangents as a special case of secant, secant to a circle, two parallel tangents at most for a given secant, non-intersecting lines and various important theorems. 

 

  • Theorems

 

This section of the NCERT CBSE Class 10 Chapter 10 teaches you various important theorems that are important from the exam point of view. They have been discussed below.

 

  • Number of Tangents Drawn from a given Point: 

 

In this section of CBSE Class 10 Maths Syllabus, you will be learning about the number of tangents drawn from a given point. Here you will learn the following.

  1. If you draw a line through a point inside the circle, then that line is a secant, and no tangent can be constructed through a point inside the circle.
  2. If you draw a line through a point on the circle, then that is a tangent. This way you can only construct one tangent
  3. From a point given outside the circle, you can draw exactly two tangents to the circle. 

This theorem has been explained to you through detailed illustrations.

 

  • Tangent Perpendicular to the radius at the point of contact

 

As per this theorem, the tangent to a circle is always perpendicular to its radius that passes through the point of contact of the tangent. 

NCERT CBSE Class 10 Maths Chapter 10 Exercise-Discussion

Our NCERT Solutions for Class 10 Maths Chapter 10 – Circles, consists of 2 exercises with a total of 17 questions. Below is the brief overview

Exercise 10.1

This exercise of NCERT Solutions for Class 10 Maths Chapter 10, consists of 4 questions. Question 1 is a short answer question, which asks about the tangents of a circle. Question 2 is fill in the blank question that covers various topics of the chapter. Question 3 is a short answer question, in which you have to find the tangent of a given point. Question 4 is based on the tangent and secant of the circle. 

Exercise 10.2

This exercise consists of 13 questions. Questions 1 to 3 is multiple-choice questions. In question 1, you will have to find the radius of the circle with given points and length of the tangents. In question 2 and question 3, you have to find the quadrilateral triangle with the given angles. Question 4 asks you to prove that tangents drawn at the ends of a diameter parallel. Question 5 has been asked from the concept of the tangent of a circle. 

Question 6 is a short answer question, which is from the radius of the circle concept. It requires you to use the theorems learnt in this chapter. Question 7 asks you to find the length of a chord based on the given information. Question 8 is based on a quadrilateral drawn to circumscribe a circle. It asks you to prove that the sum of two parallel sides of the quadrilateral is equal to the sum of the other two parallel sides of the quadrilateral.

Question 9 is from parallel tangents to a circle, where you will have to prove that the given angle is 90 degrees or not. Question 10 is based on the angle of the tangent. Question 11 is based on a rhombus. Question 12 asks you to find the sides of a triangle with the given radius and length. Question 13 is based on quadrilateral circumscribing a circle. Most questions of this exercise are application-based questions based on various concepts of the chapter.