# Circles Chapter 10 Class 10 Maths NCERT Textbook With Solutions PDF

NCERT Solutions for Class 10 Maths Chapter 10′ PDF Quick download link is given at the bottom of this article. You can see the PDF demo, size of the PDF, page numbers, and direct download Free PDF of ‘Ncert Class 10 Maths Chapter 8 Exercise Solution’ using the download button.

### Chapter 10: Circles

#### 10.1 Introduction

You have studied in Class IX that a circle is a collection of all points in a plane that are at a constant distance (radius) from a fixed point (center).

You have also studied various terms related to a circle like a chord, segment, sector, arc, etc. Let us now examine the different situations that can arise when a circle and a line are given in a plane.

#### 10.2 Tangent to a Circle

In the previous section, you have seen that a tangent* to a circle is a line that intersects the circle at only one point.

10.3 Number of Tangents from a Point on a Circle

To get an idea of the number of tangents from a point on a circle, let us perform the following activity

#### 10.4 Summary

In this chapter, you have studied the following points :

1. The meaning of a tangent to a circle.
2. The tangent to a circle is perpendicular to the radius through the point of contact.
3. The lengths of the two tangents from an external point to a circle are equal.

### NCERT Solutions Class 10 Maths Chapter 10 Circles

1. How many tangents can a circle have?

There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal distance from a point. Since there are infinite points on the circumference of a circle, infinite tangents can be drawn from them.

2. 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 …………

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

(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.

3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at

a point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm

(B) 13 cm

(C) 8.5 cm

(D) √119 cm

In the above figure, the line that is drawn from the center of the given circle to the tangent PQ is perpendicular to PQ.

And so, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get,

OQ2 = OP2+PQ2

(12)= 52+PQ2

PQ2 = 144-25

PQ2 = 119

PQ = √119 cm

So, option D i.e. √119 cm is the length of PQ.

4. Draw a circle and two lines parallel to a given line such that one is a tangent and the

other, a secant to the circle.