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RD Sharma Class 10 Math Circles Solutions - Free PDF Download

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Last updated date: 17th Apr 2024
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Free PDF download of RD Sharma Solutions for Class 10 Maths Chapter 10 - Circles

Free PDF download of RD Sharma Solutions for Class 10 Maths Chapter 10 - Circles solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 10 - Circles Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register for online coaching for JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. Every NCERT Solution is provided to make the study simple and interesting on Vedantu.


Register Online for Class 10 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu.com is No.1 Online Tutoring Company in India Provides you Free PDF download of NCERT Solutions for Class 10 Maths solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Chapter wise Questions with Solutions to help you to revise complete Syllabus and Score More marks in your examinations.

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Class 10 Maths Chapter 10 RD Sharma Solutions - Circles

‘Circles’ as Chapter 10 of R. D. Sharma class 10 Maths is an important chapter related to Geometry and every year, short to long type questions are asked in the class 10 Board exams. A circle is the set of all points in the plane that are at a fixed distance (the radius) from the fixed point (the center). Any interval joining a point on the circle to the center is called the radius so by definition, any two radii have the same length.  Some of the important terms related to the Circle are :

  • Center as the fixed point in the circle

  • Radius (R)

  • Diameter (D) passing through the center and denoted as D=2R

  • Circumference as the perimeter of the circle denoted as C= 2πR

  • Arc divided into major arc (longer arc created by two points) and minor arc (shorter arc created by two points)

  • Sector by joining the arc to the center: major sector and minor sector (considered by default)

  • Semi-Circle which is half of a circle


Apart from the above features/properties of a circle, there are some other properties related to Lines in a Circle and the Angles in a Circle:


Important Properties- Lines in a Circle

  • A Chord whose endpoints lie on the boundary of the Circle. The Diameter is assured to be the longest chord. Its property includes a perpendicular dropped from the center that divides the chord into two equal parts.

  • A Tangent that touches the circle at any point. Its property includes a radius always being perpendicular to the tangent at which it touches the circle.


Important Properties- Angles in a Circle

  • An Inscribed Angle formed between two chords when they meet on the boundary of the circle. Its properties include angles formed by the same arc on which the circumference of the circle is always equal and the angle in a semicircle is always 90°.

  • A Central Angle formed when two-line segments meet such that one of the endpoints of both the line segments is at the center and the other on the boundary of the circle. Its property includes an angle formed by the arc at the centre is twice the inscribed angle formed by the same arc.

FAQs on RD Sharma Class 10 Math Circles Solutions - Free PDF Download

1. What are the important formulae to remember while studying Circles?

All of the formulae used to calculate certain features of the circles are related to one another hence it is very easy to memorize the formulae while practicing questions on the same. Some of the formulae are as follows:

  • Circumference: C= 2πR (where R is the radius of the circle)

  • Diameter: D=2R

  • Length of an arc: central angle made by the arc/360°x (2πR)

  • Area of the circle: πR2

  • Area of a sector:  centra*l angle by the sector/360°x (πR2 )

2. Where do we find the best resources for solving questions on Circles?

R. D. Sharma class 10 Maths stands out as the best textbook with excellent questions in the form of exercises after the chapter is completed. As suggested by experts, the examples have been explained in simple words so that students can understand why and how each step of the solution has been used to solve a particular question. NCERT is also another recommended textbook by CBSE. For tips and tricks, study materials from Vedantu are also available for free and can be downloaded from the official website.

3. How do we study the formulae of Circles?

Formulae of the circles mostly revolve around the radius, diameter and   circumference of the circles. The most important aspects of the chapter are the area of the circle and the sector. Since the formulae are not very difficult to remember, easy derivation of each formula and understanding of the concepts of the chapter are more than enough for retaining the formulae in mind ahead of the exam. If needed, short notes can be made on the modules of the chapter which could help in strengthening the grasp over the topics.

4. How many exercises are there in R. D. Sharma class 10 Maths book?

Circles has been added as the 10th chapter in R. D. Sharma class 10 Maths book. This chapter consists of two exercises which include area of the arc and sector, angles in the circle, properties of a tangent in a circle, lengths and distance of tangent from a point on the circle, cyclic quadrilateral and other types of tangents as well as concentric circles. Each of these questions are worded in different ways for students to analyze and find the right solutions.  

5. Are the exercises after completion of chapter enough to score well in class 10 Maths Board Exam?

Rome wasn't built in a day and hence it takes lots of time , patience and  efforts to create something monumental and worth remembering. The same can be applied for Maths in which good scores can be only achieved through regular practice.  It is mandatory for students to solve examples, exercise after every chapter, Previous Years’ question papers and sample/mock papers to get a fair idea of the type of questions that might come in the exam. Special importance has to be given to formulae in every chapter because that is the base for solving Maths-related questions.