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## NCERT Class 9 Maths Textbook Chapter 10 With Answer Book PDF Free Download

### Chapter 10: Circles

#### 10.1 Introduction

You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50 p, Re 1, and Rs 5, key rings, buttons of shirts, etc. (see Fig.10.1).

In a clock, you might have observed that the second’s hand goes around the dial of the clock rapidly and its tip moves in a round path.

This path traced by the tip of the second hand is called a circle. In this chapter, you will study circles, other related terms, and some properties of a circle

#### 10.2 Circles and Its Related Terms: A Review

Take a compass and fix a pencil in it. Put its pointed leg on a point on a sheet of paper. Open the other leg to some distance.

Keeping the pointed leg on the same point, rotate the other leg through one revolution.

What is the closed figure traced by the pencil on paper? As you know, it is a circle (see Fig.10.2). How

did you get a circle?

You kept one point fixed (A in Fig.10.2) and drew all the points that were at a fixed distance from A. This gives us the following definition:

Author | NCERT |

Language | English |

No. of Pages | 20 |

PDF Size | 618 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 9 Maths Chapter 9 Circles

**Exercise: 10.1 (Page No: 171)**

**1. Fill in the blanks:**

**(i) The centre of a circle lies in ____________ of the circle. (exterior/ interior)**

**(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)**

**(iii) The longest chord of a circle is a _____________ of the circle.**

**(iv) An arc is a ___________ when its ends are the ends of a diameter.**

**(v) Segment of a circle is the region between an arc and _____________ of the circle.**

**(vi) A circle divides the plane, on which it lies, in _____________ parts.**

**Solution:**

(i) The center of a circle lies in the **interior **of the circle.

(ii) A point, whose distance from the center of a circle is greater than its radius lies on the **exterior **of the circle.

(iii) The longest chord of a circle is the **diameter** of the circle.

(iv) An arc is a **semicircle **when its ends are the ends of a diameter.

(v) Segment of a circle is the region between an arc and **chord **of the circle.

(vi) A circle divides the plane, on which it lies, into **3 (three)** parts.

**2. Write True or False: Give reasons for your Solutions.**

**(i) Line segment joining the center to any point on the circle is a radius of the circle.**

**(ii) A circle has **only a **finite number of equal chords.**

**(iii) If a circle is divided into three equal arcs, each is a major arc.**

**(iv) A chord of a circle, which is twice as long as its radius, is the diameter of the circle.**

**(v) Sector is the region between the chord and its corresponding arc.**

**(vi) A circle is a plane figure.**

**Solution:**

(i) **True.** Any line segment drawn from the center of the circle to any point on it is the radius of the circle and will be of equal length.

(ii) **False.** There can be infinite numbers of equal chords in a circle.

(iii) **False.** For unequal arcs, there can be major and minor arcs. So, equal arcs on a circle cannot be said as a major arc or minor arc.

(iv) **True. **Any chord whose length is twice as long as the radius of the circle always passes through the center of the circle and thus, it is known as the diameter of the circle.

(v) **False. **A sector is a region of a circle between the arc and the two radii of the circle.

(vi) **True. **A circle is a 2d figure and it can be drawn on a plane.

NCERT Class 9 Maths Textbook Chapter 10 With Answer Book PDF Free Download