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## NCERT Class 10 Maths Textbook Chapter 10 With Answer Book PDF Free Download

### 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 :

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

Author | NCERT |

Language | English |

No. of Pages | 10 |

PDF Size | 333 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 10 Maths Chapter 10 Circles

**1. How many tangents can a circle have?**

**Answer:**

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 …………**

**Answer:**

(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**

**Answer:**

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,

OQ^{2} = OP^{2}+PQ^{2}

(12)^{2 }= 5^{2}+PQ^{2}

PQ^{2} = 144-25

PQ^{2} = 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.**

**Answer:**

In the above figure, XY and AB are two parallel lines. The line segment AB is the tangent at point C while the line segment XY is the secant.

NCERT Class 10 Maths Textbook Chapter 10 With Answer Book PDF Free Download