**NCERT Solutions Class 9 Maths Chapter 10 Circles** – Here are all the NCERT solutions for Class 9 Maths Chapter 10. This solution contains questions, answers, images, explanations of the complete Chapter 10 titled Circles of Maths taught in class 9. If you are a student of class 9 who is using NCERT Textbook to study Maths, then you must come across Chapter 10 Circles. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 9 Maths Chapter 10 Circles in one place.

## NCERT Solutions Class 9 Maths Chapter 10 Circles

Here on **AglaSem Schools**, you can access to **NCERT Book Solutions** in free pdf for Maths for Class 9 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 10 Circles , Maths, Class 9.

Class | 9 |

Subject | Maths |

Book | Mathematics |

Chapter Number | 10 |

Chapter Name |
Circles |

### NCERT Solutions Class 9 Maths chapter 10 Circles

Class 9, Maths chapter 10, Circles solutions are given below in PDF format. You can view them online or download PDF file for future use.

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### NCERT Solutions Class 9 Maths chapter 10 Circles- Video

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### Download NCERT Solutions Class 9 Maths chapter 10 Circles In PDF Format

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### Question & Answer

Q.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.

Ans :(i) The centre of a circle lies ininteriorof the circle. (ii) A point, whose distance from the centre Of a circle is greater than its radius lies Inexteriorof the circle. (iii) The longest chord of a circle is adiameterof the circle. (iv) An arc is a semi-circle when its ends are the ends of a diameter. (v) Segment of a circle is the region between an arc andchordof the circle. (vi) A circle divides the plane, on which it lies, inthreeparts.

Q.2:Write True or False: Give reasons for your answers. (i) Line segment joining the centre to any point on the circle is a radius of the circle. (ii) A circle has only 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 a diameter of the circle. (v) Sector is the region between the chord and its corresponding arc. (vi) A circle is a plane figure

Ans :(i) True. All the points on the circle are at equal distances from the centre of the circle, and this equal distance is called as radius of the circle. (ii) False. There are infinite points on a circle. Therefore, we can draw infinite number of chords of given length. Hence, a circle has infinite number of equalchords. (iii) false. Consider three arcs of same length as AB, BC, and CA. It can be observed that for minor arc BOC, CAB is a major arc. Therefore, A3, BC, and CA are minor arcs of the circle. (iv) True. Let AB be a chord which is twice as long as its radius. It can be observed that in this situation, our chord will be passing through the centre of the circle. Therefore, it will be the diameter of the circle. (v) False. Sector is the region between an arc and two radii joining the centre to the end points of the arc. For example, in the given figure, OAB is the sector of the circle. (vi) True. A circle is a two-dimensional figure and it can also be referred to as a plane figure.

Q.3:Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Ans :A circle is a collection of points which are equidistant from a fixed point. This fixed point is called as the centre of the circle and this equal distance is called as radius of the circle. And thus, the shape of a circle depends on its radius. Therefore, it can be observed that if we try to superimpose two circles of equal radius, then both circles will cover each other. Therefore, two circles are congruent if they have equal radius. Consider two congruent circles having centre O and O' and two chords AB and CD of equal lengths. In \( \triangle \mathrm{AOB}\) and \( \triangle \mathrm{CO'D}\) AB = CD (Chords of same length) OA = O'C (Radii of congruent circles) 0B = O'D (Radii of congruent circles) \( \triangle \mathrm{AOB}\) \( \triangle \mathrm{CO'D}\) (SSS congruence rule) \( \angle A O B=\angle C O^{\prime} D\) (By CPCT) Hence, equal chords of congruent circles subtend equal angles at their centres.

Q.4:Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Ans :In \( \triangle \mathrm{AOB}\) and \( \triangle \mathrm{CO'D}\) \( \angle A O B=\angle C O^{\prime} D\) (given) OB = O'D (Chords of same length) OA = O'C (Radii of congruent circles) \( \triangle \mathrm{AOB}\) \( \triangle \mathrm{CO'D}\) (SSS congruence rule) AB=CD (By CPCT) Hence , if the chord of congruent circle equal angles at their centers, then the chords are equals.

Q.5:Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Ans :Consider of the following pair of circles. The above circles do not intersect each other at any point . therefore, they do not have any point in common. The above circles touch each other only at one point Y. therefore, there is 1 point in common. The above circles touch each other at 1 point X only. Therefore the circles have one point in common. These circles intersect each other at two points G and H. Therefore, the circles have two points in common. It can be observed that there can be a maximum of 2 points in common. Consider the situation in which two congruent circles are superimposed on each other. This situation can be referred to as if we are drawing the circle two times.

## NCERT / CBSE Book for Class 9 Maths

You can download the NCERT Book for Class 9 Maths in PDF format for free. Otherwise you can also buy it easily online.

- Click here for NCERT Book for Class 9 Maths
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### All NCERT Solutions Class 9

- NCERT Solutions for Class 9 English
- NCERT Solutions for Class 9 Hindi
- NCERT Solutions for Class 9 Maths
- NCERT Solutions for Class 9 Science
- NCERT Solutions for Class 9 Social Science
- NCERT Solutions for Class 9 Sanskrit

### All NCERT Solutions

You can also check out NCERT Solutions of other classes here. Click on the class number below to go to relevant NCERT Solutions of Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Class 1 | Class 2 | Class 3 |

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