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RD Sharma Class 10 Chapter 10 Solutions (Circles)

In RD Sharma Class 10 Maths Solutions Chapter 10 – Circles you will learn about Circles and its properties and existence of the tangents to a circle. You will also come to know about some complex terms such as tangents, tangents of a circle, number of tangents passing from a given point on the circle. This Chapter is exciting for students because of the involvement of geometrical calculations and diagrams.

Our Solutions for the Chapter RD Sharma Class 10 Maths Solutions Circles have been carefully drafted for all the 13 questions asked in the Chapter. The questions are based on the properties of Circles and tangents. Here you will learn how to answer the direct questions related to tangents. You will also learn to relate the fact that tangent to a Circle is perpendicular to the radius through the point of contact while answering some of the word problems. Here you will also learn to use the fact that lengths of the two tangents from an external point to a circle are equal while devising a strategy to answer some questions.

The carefully curated Solutions of RD Sharma Class 10 Maths Chapter 10 provides a thorough understanding of the chapter. All the questions are answered in a comprehensive manner. Our RD Sharma Solutions make the learning process exciting and prepare you well for your CBSE board exams.

RD Sharma Class 10 Maths Circles: Important Topics

Class 10 Maths Circles tell you that Circle is an assembly of all points in a plane placed at a persistent distance (radius) from a fixed point called the centre. Here you learn the concepts of circles, tangent to a Circle and number of tangents from a point on a circle. The detailed description of the topics dealt in this Chapter is given below.

 

  • Tangent to a Circle

 

Here you learn that the line which touches or intersects any Circle at only one point is known as the tangent to a circle. The common point of a given tangent and the Circle is called the point of contact.

Further, you learn that there is only one tangent at a point of the Circle and the tangent passing through a point on a Circle is a distinct case of a secant, where the two endpoints of the chord corresponding to it coincide.

Next, this chapter teaches you the theorem, which says that the tangent passing through a specific point of a Circle is at a right angle to the radius over the point of contact. This theorem concludes that at any point on a circle, there can be one and only one tangent. You further come to know that the line containing the radius through the point of contact is called the ‘normal’ to the Circle at the point.

 

  • Number of Tangents from a Point on a Circle

 

In this portion of the Chapter, you will learn about three cases regarding tangents which are-

  1. No tangent passing through a point on a Circle can lie inside the circle, 
  2. Only one tangent to a Circle passes through a point lying on that Circle and 
  3. There are specifically two tangents to a circle through a point lying outside the circle. 

Further, you learn here that the length of the segment of the tangent from an outer point P and the specific point of contact lies on the Circle is called the length of the tangent from the point P to that circle. This chapter teaches you a theorem that states that the lengths of tangents drawn from an external point to a circle are equal.

RD Sharma Class 10 Maths Chapter 10: Exercise-Discussion

There are 2 exercises in this Chapter of RD Sharma Class 10 Maths Book. The components of these exercises are given below –

Exercise 10.1

This exercise consists of 4 questions. Question 1 is fill in the blank type question. Question 2 is a direct question on tangents. Questions 3 and 4 are word problems, and they ask you to determine the radius of the circle.

Exercise 10.2

The second exercise contains 9 questions. Questions 1 and 2 are word problems asking you to determine the length of the tangent. Question 3 is a word problem asking you to calculate the radius of the given Circle when the length of a tangent drawn to the Circle is given. 

Questions 4 and 5 ask you to prove some equalities based on the properties of the circle. Question 6 asks you to find the perimeter of a triangle formed by two tangents drawn on a circle. Question 7 asks you to prove some facts regarding tangents drawn on the given circle. Question 8 and 9 ask you to determine values of angle and length of a chord in a Circle given in respective questions.

Benefits of RD Sharma Class 10 Maths Solutions for Chapter 10 – Circles

  • Our Solutions cover all the topics and subtopics of this Chapter and give meticulous and detailed answers to all the above questions of the exercises.
  • Our Solutions provide the best answers to the questions maintaining the logical flow and at the same are easy to understand and grasp. 
  • Our RD Sharma Solutions are fully accurate, to the point and facilitate quick and effective learning.
  • They are the best study material available to clear your concepts related to Circles.
  • You will find the content interesting, engaging and well structured.
  • Our RD Sharma Solutions help you become thorough with the concepts of the Chapter through an ample amount of practice. 
  • Our Maths shortcuts and innovative study techniques help you instantly clear all your doubts and remember for a longer period of time. 
  • Our Solutions will help you to prepare in the best way for securing maximum marks in Class 10 board examination.