# NCERT Solutions for Class 10 Maths Chapter 10

NCERT Solutions for class 10 Maths Chapter 10 Circles all Exercises in English Medium and Hindi Medium or View in Video Format for CBSE, UP Board as well as MP Board students. These solutions are applicable for the session 2021-22 onward. Students can download 10th Maths Solutions in PDF format free to use offline. UP Board students are now using NCERT Books for their exams. So, they can download UP Board Solutions for Class 10 Maths Chapter 10 all exercise from this page of Tiwari academy. Download UP Board Solution and NCERT Solutions Apps 2021-22 based on latest NCERT Books for academic session 2021-2022.

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### 10th Maths Chapter 10 Exercise 10.1

### 10th Maths Chapter 10 Exercise 10.2

Class: 10 | Maths (English and Hindi Medium) |

Chapter 10: | Circles |

### 10th Maths Chapter 10 Solutions

NCERT Solutions for class 10 Maths Chapter 10 Circles is given here to free download in PDF or use online without downloading. Download UP Board Solutions for Class 10 Maths which are updated for current academic session 2021-22 for all students who are using latest NCERT Books 2021-22.

#### Class 10 Maths Exercise 10.1 Solution in Hindi Medium Video

#### Class 10 Maths Exercise 10.1 Explanation and Solutions in Videos

#### Class 10 Maths Exercise 10.2 Solution in Hindi Medium Video

#### Class 10 Maths Exercise 10.2 Explanation and Solutions in Videos

### NCERT Solutions for Class 10 Maths Chapter 10

- NCERT Solutions 10th MathsExercise 10.1Read more
- NCERT Solutions 10th MathsExercise 10.2Read more

#### Previous Years Questions

ONE MARK QUESTIONS

1. Prove that tangents drawn at the ends of a diameter of a circle are parallel to each other. [CBSE 2017]

THREE MARKS QUESTIONS

1. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angle PTQ = 2 (angle OPQ). [CBSE 2017]

FOUR MARKS QUESTIONS

1. Prove that the lengths of tangents drawn from an external point to a circle are equal. [CBSE 2017]

##### Historical Facts!

- The circle is the most primitive and rudimentary of all human inventions. It is the corner stone in the foundation of science and technology. It is the basic tool used by greatest artists and architects in the history of mankind.
- The ancient Indian symbol of a circle, with a dot in the middle, known as ‘BINDU’ was probably instrumental in the use of circle as a representation of the concept zero.
- The ratio of the circumference of a circle to its diameter is always a constant. This constant is universally denoted by Greek letter π.

##### Which exercise from 10th Maths chapter 10, helps to score more in exams?

There are two exercises in class 10 Maths chapter 10. Exercises 10.2 contains all the important questions which are generally asked in school tests and board exams also. The last 5 questions given in ex. 10.2 is really very good questions to asked in exams.

##### What do you understand by a Circle and tangent to a circle in class 10 Maths Chapter 10?

Circle: A circle is the set of points in a plane which are at the same distance from a fixed point in the plane. The fixed point is called the centre of the circle and the line segment joining the centre & a point on circle is called radius.

Tangent to a circle: If a line drawn in the plane of a circle intersects the circle in one and only one point, then the line is called a tangent to the circle and the point at which the line intersect the circle is called the point of contact of the line with the circle.

##### How many theorems are there in Class 10 Chapter 10 Circles to prove?

There are two theorems which asked in board exams to prove.

Theorems on tangent to a circle:

(i). A tangent to a circle is perpendicular to the radius drawn from point of contact or A line drawn perpendicular to a radius at its end point on the circle is a tangent to the circle.

(ii). the tangents drawn to a circle from a point in the exterior of the circle are equal in length or the lengths of tangents drawn from an external point to a circle are equal.

##### How many exercises are there in class 10 chapter 10 Circles?

There are 2 exercises in class 10 chapter 10 Circles.

In first exercise (Ex 10.1), there are only 4 questions.

In second exercise (Ex 10.2), there are in all 13 questions.

So, there are in all 17 questions in class 10 chapter 10 Circles.

There are only 3 examples (example 1, 2 and 3) in class 10 chapter 10 Circles.

##### What students will study in chapter 10 Circles of class 10 Maths?

In chapter 10 Circles of class 10 maths, students will study:

1) Meaning of Tangent to a Circle.

2) Meaning of Secant of the circle.

3) Point of Contact.

4) Theorem 10.1 “The tangent at any point of a circle is perpendicular to the radius through the point of contact”.

5) Number of Tangents from a Point on a Circle.

6) Length of the Tangent.

7) Theorem 10.2 “The lengths of tangents drawn from an external point to a circle are equal.”

##### Which theorem can be asked in exam for proof from chapter 10 Circles of 10th Math?

There are only two theorems in chapter 10 Circles of 10th Math and proof of any theorem can come in exam because both the theorems are equally important from exam point of view. For exams students should prepare both the theorems.

##### How much time students need to go through the chapter 10 of class 10th math?

Students need maximum 6-7 days to complete chapter 10 (Circles) of class 10th mathematics if they are giving 1 hour per day to chapter 10. Also this time depends on student’s speed, capability and many other factors.