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# NCERT Exemplar Class 10 Maths Chapter 9 Solutions: Circles

NCERT Exemplar Class 10 Maths Solutions for Chapter 9 ‘Circles’ are prepared in order to guide you in solving the exemplar exercises. This chapter of NCERT Class 10 Maths Exemplar is majorly a meditation on the tangents to a circle and angles formed by them at different points. You will get to learn about various theorems about tangents to a circle and their point of contact in this chapter. With the help of these theorems, you can further devise other results and theorems to be used in other topics of geometry.

There are a total of 44 questions covered in 4 exercises in this chapter. The questions are of diverse variety such as true or false, fill in the blanks, reasoning and verification questions. Thus, the exercises are designed to cover all the topics in detail. The theorem-based questions will require you to prove some results that you can also use in the chapters ahead and will remain a part of your curriculum until higher classes.

The answers to all the NCERT Class 10 Exemplar problems for Chapter 9 Class 10 Maths are written in simple language by our subject matter experts. We, at Instasolv, provide you with highly reliable solutions that are accurate as well as precise in nature. Thus, if you practice our exemplar exercise questions using our solutions as your source of reference, you will move ahead with a strong foundation in geometrical maths.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 9: Circles

Introduction

1. If a line passes from near a circle without touching it at any point, it is non-intersecting with respect to the given circle.
2. If a line passes through the given circle intersecting it at 2 points forming a chord in the circle, then the line is termed as secant with respect to the circle.
3. If a line passes through the given circle intersecting it at 1 point and hence, just touching the circle, then the line is known as the tangent with respect to the circle.

Thus, we can also conclude that the tangent is a special case of a secant, with respect to the circle when the two ends of the chord formed by it coincide at one point.

Theorem 1

If we draw a tangent at any point of the circle, the radius drawn through it to that point is perpendicular to the tangent.

Theorem 2

Firstly, we must understand that only two tangents can be drawn to a circle from a point that lies outside the circle.

Now, if we draw tangents to a circle from one point lying externally with respect to the circle, the lengths of the two tangents will be equal.

Using the above theorem, we can also derive the Pythagoras theorem.

Theorem 3

If we consider two circles with the same centre, the chord of the larger circle which is tangential to the smaller circle will be bisected at the point of contact with the smaller circle.

### Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 9: Circles

1. The first exercise, 9.1 consists of multiple-choice questions. These questions cover all the theorems of this chapter and will require you to evaluate the values of lengths of tangents as well as the angles formed by them.
2. In exercise 9.2, 10 statements are given such that you will have to check if they are true or false based on topics such as tangents of a circle, the angle between tangents, perpendicular bisectors, etc.
3. Exercise 9.3 comprises questions based on figures. You will be able to find the results of these questions by applying a combination of concepts learned in previous classes and this chapter.
4. Lastly, in exercise 9.4, there are 14 long answer type questions in which you will get to find relations between sides of a hexagon circumscribing a circle, relationship between chords, diameters and different angles formed by the tangents.