CLASS 10 MATHS NCERT SOLUTION CHAPTER 12 PDF Areas Related to Circles

**NCERT Solutions of Class 10 Maths**

**NCERT Solutions for Class 10 Maths All Chapters**

Find NCERT Solutions for Class 10 Maths App all Chapters, which are provided by the expert math teacher. You just need to click simply these below mentioned Exercise-wise links here and get the solutions. You can get solutions for all topics of the NCERT Class 10 book here with both modes offline and online. These Chapter Wise NCERT Solutions for Class 10 Maths are also available here in both medium Hindi and English here. And just download here Class 10 Maths Chapter Wise Solutions in PDFs, you can share these solutions to your friends to help him/her. Here you also get NCERT Exemplar Class 11 Maths Solutions which provide you best idea of your board exam question pattern, so that you can solve all the questions easily in your exam. By doing well practice with these free Class 10th Maths Solutions, you can pass your 10th board exam with good percentage. Join us for latest CBSE Class 10 information and other educational news.

**NCERT Class 10 Maths all Chapters Solution**

There are 15 chapters in NCERT Class 10 Book, and here you can get solutions for all chapters provided by the skilled Maths teacher. Practicing these textbook exercises will help the students in their preparation for the board examination. Class 10 Maths is the most important subject, and you need to do well practice so that you can solve the higher class’s math sums easily. The chapters covered in this NCERT Solutions for Class 10 Maths are as Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Some Applications of Trigonometry, Constructions, Surface Areas and Volumes, Statistics Probability. UP Board students are also using NCERT Books, they also can download UP Board Solution for Class 10 Maths.

There are two exercises in this chapter. NCERT solutions for class 10 Maths chapter 15 Probability covers the concept of probability, Simple problems on finding the probability of an event, the difference between experimental probability and theoretical probability etc. Download here FREE unlimited NCERT solutions for class 10 mathematics Probability PDF, and enjoy the flexible learning at any time. Each and every solution are well solved to be the experienced math teacher. Here students can also download Chapter Probability class 10 Maths solutions in Hindi medium and English medium.

**How to Prepare Class 10 Maths All Chapters**

**Chapter 1: Real Numbers**

In this NCERT Solutions for Class 10 Maths Chapter 1, Real Numbers, students learn about the “Real Numbers “In mathematics language, there are two kinds of numbers- one is the “real number”, and another one is the “imaginary number”. In the number system, Real numbers are just the combination of rational and irrational numbers. These can be represented in a number line. And where the imaginary numbers are the unreal numbers, theses cannot be expressed in the number line which is used to represent a complex number. A real number can be a positive or negative and which are denoted by the symbol “R”.

**Summary:** Definition, Set of real numbers, Chart, Properties, Commutative, Distributive, and Identity.

**Chapter 2: Polynomials**

In this NCERT Solutions for Class 10 Maths Chapter 2, Polynomials, you learn about Polynomials which are as expressions composed of two algebraic terms. Polynomials contain two or more algebraic terms. Poly means many and Nominal means term. Polynomials are composed as Constants such as 1, 2, 3, etc., Variables such as g, h, x, y, etc., Exponents such as 3in x3 etc. And here you also learn the degree of a polynomial is defined as the highest degree of a monomial within a polynomial. Polynomials are of 3 different types such as Monomial, Binomial, Trinomial etc. And Polynomial Properties and Theorems are explained in this chapter.

**Summary:** Definition, Degree, Terms, Types, Properties and Theorems, Equations, Function, Solving Polynomials, Operations etc.

**Chapter 3: Pair of Linear Equations in Two Variables**

In this NCERT Solutions for Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables, student learn about Pair of Linear Equations with the form ax + by + c = 0, In this equation a, b and c are real numbers and where a, b not equal to zero then this equation is known as linear equation in two variables. Here you also learn about Linear Equations in Two Variables Word Problems.

**Summary:** Definition, Linear Equations Formula, Linear Equations in Two Variables Example, Linear Equations in Two Variables Word Problems etc.

**Chapter 4: Quadratic Equations**

In this NCERT Solutions for Class 10 Maths Chapter 4, Quadratic Equations, You learn about Quadratic Equations, the name Quadratic comes from “quad” Meaning Square, as the variable gets squared (like x2). Quadratic Equations is also called an “Equation of Degree”. The Standard Form of a Quadratic Equation looks is like: Quadratic Equation: ax2 + bx + c = 0, where a, b and c are known values. “a” can’t be 0.

**Summary:** Definition, Hidden Quadratic Equations, Using the Quadratic Formula, Complex Solutions,

**Chapter 5: Arithmetic Progression**

In this NCERT Solutions for Class 10 Maths Chapter 5, Arithmetic Progression, You learn about Arithmetic Progression which is also known as “AP”. It is an order of the difference of any two successive numbers is a constant value. Here you can see a common difference odd numbers and even numbers. You come across Arithmetic progression in this chapter.

**Summary:** Definition, Common Difference, First Term, General Form, Nth Term, Sum of Nth Term, Formula List etc.

**Chapter 6: Triangles**

Here in this NCERT Solutions for Class 10 Maths Chapter 6, Triangles, the student can learn about “Triangles “ which have a three-sided polygon that consists of 3edges and three vertices. A triangle is a type of polygon. Here you also learn about property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees etc. Triangles are of 6 types. Learn about its properties, Heron’s Formula to find the area, various formulas such as perimeter and area defined for the triangle.

**Summary:** Definition, Types of Triangles, Properties of Triangle, Pythagoras Theorem, Triangle Formula.

**Chapter 7: Coordinate Geometry**

Here in this NCERT Solutions for Class 10 Maths Chapter 7, Coordinate Geometry student learn about Coordinate Geometry which describes the link between geometry and algebra by the use of graphs, curves and lines. You can solve geometric problems with geometric aspects in Algebra. Coordinate geometry is defined as the study of geometry by using the coordinate points. You can find the distance between two points, dividing lines, midpoints, area of triangle etc.

**Summary:** Coordinate Geometry Definition, Distance Formula, Mid-Point Theorem, Section Formula, Equation of a Line in Cartesian Plane, Coordinate Geometry Formulas and Theorems etc.

**Chapter 8: Introduction to Trigonometry**

Here in this NCERT Solutions for Class 10 Maths Chapter 8, Introduction to Trigonometry, you study about the complete concept on trigonometry. Here you learn all about Trigonometric Ratios, Opposite & Adjacent Sides in a Right Angled Triangle, Trigonometric Ratios, Visualization of Trigonometric Ratios Using a Unit Circle, Relation between Trigonometric Ratios, Range of Trigonometric Ratios from 0 to 90 degrees such as tanθ and secθ are not defined at 90∘.

cotθ and cosecθ are not defined at 0∘. And also know sin (90∘−θ) = cos θ,cos (90∘−θ) = sin θ, tan (90∘−θ) = cot θ and many more.

**Summary:** Introduction to Trigonometry, Trigonometric Ratios, Visualization of Trigonometric Ratios Using a Unit Circle, Relation between Trigonometric Ratios, Trigonometric Ratios of Specific Angles etc.

**Chapter 9: Some Applications of Trigonometry**

Here in this NCERT Solutions for Class 10 Maths Chapter 9, Some Applications of Trigonometry, you study about “Trigonometry” which is defined as calculations with triangles including the study of lengths, heights, and angles. The function of Trigonometry is used in our daily life, such as distance between landmarks, astronomy to the measurement of the satellite navigation system. Trigonometry is used in many fields such as engineering, physics, surveyors, architects, astronauts. And most interesting, trigonometry is also used in developing computer music.

**Summary:** What is Trigonometry, Trigonometry Applications in Real Life, Trigonometry to Measure Height of a Building or a Mountain, Trigonometry in Aviation, Trigonometry in Criminology, and Trigonometry in Marine Biology etc.

**Chapter 10: Some Applications of Circles**

In this NCERT Solutions for Class 10 Maths Chapter 10, Some Applications of Circles, you learn about the circle which is a special kind of ellipse in which the eccentricity is zero and also circle is drawn the points at an equidistant from the centre, distance from the center of the circle is known as the radius and twice of the radius is known as diameter. The circle has rotational symmetry around the centre for every angle. Annulus, Arc, Sector, Segment, Centre, Chord, Diameter, Secant, Tangent are the terminologies of the circle.

**Summary:** Circle Definition, How to draw a circle, Circles Terminologies, Circle Formulas for Area and Circumference, Circle Area Proof, Properties of Circles etc.

**Chapter 11: Construction**

In this NCERT Solutions for Class 10 Maths Chapter 11, Construction, You can learn about how to construct the division of the line segment, constructions of tringles by the use of scale factor, construction of tangents to a circle. And know how to Dividing a Line Segment such as: Bisecting a Line Segment, Constructing a Similar Triangle with a scale factor, Drawing Tangents to a Circle, Number of Tangents to a circle, Drawing tangents to a circle from a point outside the circle etc. By well practice this chapter “Construction”, you will learn how to construct the various diagram.

**Summary:** Constructions, Drawing Tangents to a Circle, Similar Triangle with a scale factor Constructions, Construction Procedure etc.

**Chapter 12: Areas Related to Circles**

In this NCERT Solutions for Class 10 Maths Chapter 12, Areas Related to Circles, You can get the full knowledge about Areas Related to Circle such as circumference, segment, sector and angle etc. Area of a circle is πr2, where π=22/7. π is the ratio of the circumference of a circle to its diameter. Here you can learn about the area for the sector of a circle.

**Summary:** Area of a Circle, Circumference of a circle, the segment of a circle, The angle of a Sector, Area of a Sector of a Circle, Area of a Segment of a Circle etc.

**Chapter 13: Surface Areas and Volumes**

In this NCERT Solutions for Class 10 Maths Chapter 13, Surface Areas and Volumes, you study the concept of surface area and volume. Here you learn all shapes of the circle: cube, cuboid, cone, cylinder, and etc. The procedure to find the volume and its surface area and the combination of different solid shapes is also learned in this chapter.

**Summary:** Cuboid and it’s Surface Area, Cube and its Surface Area, Cylinder and it’s Surface Area, Right Circular Cone, and it’s Surface Area, Sphere and its Surface Area, Volume of a Cuboid etc.

**Chapter 14: Statistics**

In this NCERT Solutions for Class 10 Maths Chapter 14, Statistics, you study here about Statistics which is the study of the collection, interpretation, presentation, analysis etc. Mathematical statistics is the application of Mathematics to Statistics, and this is used in collection & analysis of facts about a country such as economy, and, military, population etc. In this chapter, you can also learn about: linear algebra, stochastic analysis, differential equation etc.

**Summary:** Scope, Methods, Types of Data, Types of quantitative data, Types of Statistics, Application, Statistics Examples etc.

**Chapter 15: Probability**

In this NCERT Solutions for Class 10 Maths Chapter 14, Probability, student get knowledge of Probability which means possibility in the occurrence of a random event. Probability has been introduced to find out how events are to happen prediction. The basic probability theory is also used in the probability distribution. Here you learn the possibility of outcomes for a random experiment.

**Summary:** Definition, Formula, Examples, Equally Likely Events, Probability Density Function, Solved Problems etc.

**Importance of Learn NCERT Solutions for Class 10 Maths from Tiwari Academy**

**NCERT Solutions for Class 10 Maths from Tiwari Academy** are designed by the expert math teacher who has many years of experiences. It provides more benefits to the class 10 students by providing topic-wise and chapter-wise detailed knowledge with an easy method. There are also many other important to learn NCERT Solutions for Class 10 Maths from us. Let us discuss below:

**Strengthens Your Basics**

All chapter of class 10 maths solutions are well designed by our experienced and professionals math experts. All topic-wise and chapter-wise answers are thoroughly researched and reviewed. Student can get more marks in their Board exam or in any competitive exam by using these solutions.

**A Quick and Effective Revision Tool**

NCERT solutions are created in such a manner that help students in the event of queries or doubts in a proper way. NCERT book is handy during exam preparation as it is the best quick and effective revision tool for your board exam.

**Develops an Ability of Student to Solve Sums**

All Maths solutions are well explained comprehensively, along with relevant and easy to understand examples. Student can have an idea of how to solve sums with step by step instructions.

**Increases Student’s Confidence**

All maths solutions are provided with proper illustrations and examples. It helps build a conceptual understanding of all exercises by providing sufficient cases, and if the student gets practise well before the exam, then they can have high confidence.

**How Class 10 Maths Solutions of NCERT Helpful for Board Exams?**

Class 10 Maths Solutions of NCERT is very helpful for Board Exams as all the questions for Basic Mathematics were picked directly from NCERT textbooks. These solutions are well designed by the experienced Maths teacher. You can find many examples related the topics so that student can clear all concepts. It is a perfect guide to help you to score good marks in Board Exams. All solutions are based on the latest CBSE syllabus.