NCERT Solutions Class 10 Maths Chapter 10

NCERT Solutions for Class 10 Mathematics Chapter 10 Circles

Practicing questions from NCERT Class 10 Mathematics Chapter 10- Circles is important to prepare for your board exams. To help students with solving NCERT book questions and cross-check their answers, Extramarks provides NCERT Solutions for Class 10 Mathematics Chapter 10. These solutions are prepared by subject experts to help students solve NCERT textbook questions with accuracy and confidence. They can rely on these reference materials for quick revision and last-minute preparation also.

NCERT Solutions for Class 10 Mathematics Chapter 10 Circles 

NCERT Solutions for Class 10 Mathematics Chapter 10 Circles are prepared as per the CBSE guidelines. The subject matter experts have kept the language simple and explained the answers with relevant examples, wherever possible. Students can access these solutions for online and offline studies.

Get Complete Details about Chapter 10 Mathematics Class 10 NCERT Solutions

Chapter 10 Circles of NCERT Class 10 Mathematics is a branch of Unit 4 Geometry. Unit 4 includes 4 multiple choice questions of 1 mark each, 2 short answer questions of 3 marks each, and 2 long type questions carrying 6 marks each. To ensure that you score 22/22 in questions from this chapter refer to NCERT solutions for Class 10 Mathematics Chapter 10. Only checking out NCERT solutions will not help. It requires practicing the concepts and tips as conveyed in the guide.

Other details about Class 10 Chapter 10 Circles

Chapter 10 Circles of NCERT Class 10 Mathematics consists of the following sub-topics:

  • Introduction 
  • Tangent to a circle
  • Number of Tangents from a point on a circle
  • Summary 

Furthermore, Chapter 10 Circles of NCERT Class 10 Mathematics comes with a set of extensive exercises. These include:

Exercise 10.1 – A total of 4 Questions out of which 1 short format question, 1 Fill in the blanks and 2 long format questions.

Exercise 10.2 – A total of 13 Questions out of which 10 long format questions, 4 descriptive types and 2 short format questions.

NCERT Solutions Class 10 Mathematics Chapter 10 will guide the students appropriately not only to master the concepts but also to solve the problems with utmost precision. This in turn will give students the much-needed confidence to solve questions in their final examination with the same accuracy.

NCERT Solutions for Class 10 Mathematics

The NCERT Solutions for Class 10 Mathematics are available for the following chapters:

[Include Chapter wise Pages]

Chapter 1 – Real Numbers

Chapter 2 – Polynomials

Chapter 3 – Pair of Linear Equations in Two Variables

Chapter 4 – Quadratic Equations

Chapter 5 – Arithmetic Progressions

Chapter 6 – Triangles

Chapter 7 – Coordinate Geometry

Chapter 8 – Introduction to Trigonometry

Chapter 9 – Some Applications of Trigonometry

Chapter 10 – Circles 

Chapter 11 – Constructions

Chapter 12 – Areas Related to Circles

Chapter 13 – Surface Areas and Volumes

Chapter 14 – Statistics

Chapter 15 – Probability

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 Here are some of the reasons why students should pick  Extramarks’ study material:

  • Extramarks’ NCERT Solutions Class 10 Mathematics Chapter 10 are prepared by subject matter experts.
  • The answers are written in simple and easy-to-comprehend language.
  • The solutions are prepared as per CBSE guidelines.
  • The solutions are self-explanatory and do not require any external assistance for studying.

Related Questions

Q1. Fill in the blanks:

 (i) A tangent to a circle intersects it in _______ point(s).

(ii) A line intersecting a circle in two points is called a _____.

(iii) A circle can have ______ parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called _____.

Ans. 

(i) A tangent to a circle intersects it in one point.

(ii) A line intersecting a circle in two points is called a secant.

(iii) A circle can have two parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called the point of contact.

Q2. A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

Ans. From this figure, we can conclude a few points which are:

(i) DR = DS

(ii) BP = BQ

(iii) AP = AS

(iv) CR = CQ

Since they are tangents on the circle from points D, B, A, and C respectively.

Now, adding the LHS and RHS of the above equations we get,

DR+BP+AP+CR = DS+BQ+AS+CQ

By rearranging them we get,

(DR+CR) + (BP+AP) = (CQ+BQ) + (DS+AS)

By simplifying,

AD+BC= CD+AB

Q3. In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠ AOB = 90°.

Ans. From the figure given in the textbook, join OC. Now the triangles △OPA and △OCA are similar using SSS congruence as:

(i) OP = OC They are the radii of the same circle

(ii) AO = AO It is the common side

(iii) AP = AC These are the tangents from point A

So, △OPA ≅ △OCA

Similarly,

△OQB ≅ △OCB

So,

∠POA = ∠COA … (Equation i)

And, ∠QOB = ∠COB … (Equation ii)

Since the line POQ is a straight line, it can be considered as the diameter of the circle.

So, ∠POA +∠COA +∠COB +∠QOB = 180°

Now, from equations (i) and equation (ii) we get,

2∠COA+2∠COB = 180°

∠COA+∠COB = 90°

∴∠AOB = 90°

FAQs (Frequently Asked Questions)

The points that make NCERT Solutions for Class 10 Mathematics Chapter 10 by Extramarks unique are:

  • These are reliable study materials curated by subject matter experts.
  • It provides solved exercises and practice questions to step up the learning experience of students and eliminate “mathematics phobia” among them. The answers are detailed with diagrams and further explanations wherever necessary.
  • The solutions are prepared as per CBSE guidelines.

You can get NCERT Solutions for Class 10 Mathematics Chapter 10 on Extramarks’ website and app.