**NCERT Solutions for Class 9 Maths Chapter 10:** In this article, we bring you the detailed **NCERT Solutions for Class 9 Maths Chapter 10 – Circles**. The CBSE Class 9 Maths Chapter 10 notes (solutions) provided here are prepared by our academic experts at Embibe. You can download the free PDF of NCERT solutions for Class 9 Maths Chapter 10 to study offline. The NCERT Solutions covers exercise 10.1, exercise 10.2, exercise 10.3, exercise 10.4, exercise 10.5, and exercise 10.6.

You can use the solutions provided here as a reference while solving the exercise questions. Besides that, these solutions will also be very handy to complete your assignments and homework on time. With all the answers in one place, you can also do your revision faster. So, go through the article to get the NCERT solutions for Class 9 Maths Chapter 10.

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Table of Contents

## NCERT Solutions For Class 9 Maths Chapter 10: Circles

The NCERT Solutions for Class 9 Maths Chapter 10 involves exercise 10.1, exercise 10.2, exercise 10.3, exercise 10.4, exercise 10.5, and exercise 10.6. Before we get into the detail, let’s look at the topics included in the Class 9 Maths chapter:

Exercise | Topics |

10.1 | Introduction |

10.2 | Circles and its related terms: A Review |

10.3 | Angle Subtended by a chord at a point |

10.4 | Perpendicular from the Centre to a Chord |

10.5 | Circle through three points |

10.6 | Equal Chords and their distances from the Centre |

10.7 | Angle Subtended by an Arc of a Circle |

10.8 | Cyclic Quadrilaterals |

10.9 | Summary |

## CBSE Class 9 Maths Chapter 10: Chapter Summary

In this chapter, students will learn about **circles,** their related terms, and the properties of a circle. A circle is a collection of points on a plane, which are equidistant from a fixed point in the plane. A circle is the locus of points equidistant from a given point. The fixed point is called the centre while the fixed distance is called the radius.

A circle divides the plane into three parts: **inside the circle, on the circle, and the area outside the circle**. In this chapter, students will learn some terms related to circles like the centre of a circle, radius, diameter, arcs, and its types – major arc and minor arc, semicircle, chords, cyclic quadrilaterals, segments, and its two types – major segment and minor segment, etc.

**Download CBSE Class 9 Maths Chapter 10 Solutions PDF**

## How To Prepare For CBSE Class 9 Maths Circles?

The Class 9 Maths Circles notes (solutions) are provided here in a simplified manner which is easy to follow and understand. Once your concepts are clear, solving the exercise questions becomes quite easy. Make the best use of the solutions provided here as you solve the exercise questions.

To boost up your performance in the exam, you can solve free **Class 9 Maths Circle questions** at Embibe. Also, students can take **CBSE Class 9 Circles Chapter-wise mock test** to test their performance. Finish the chapter in the most effective manner so that you can solve any question asked.

## CBSE Class 9 Maths Chapter 10 Important Questions

Some of the important questions from this chapter are as under:

Important Questions From Circles |

- Bisectors of angles A, B, and C of a triangle ABC intersect its circumcircle at D, E, and F respectively. Prove that the angles of the triangle DEF are 90° – (½)A, 90° – (½)B and 90° – (½)C.
- In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.
- Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.
- If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lies on the third side.
- Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6, find the radius of the circle.
- If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
- ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
- A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed, and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.
- Prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal.
- Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the center.
- AC and BD are chords of a circle which bisect each other. Prove that
**(i)**AC and BD are diameters**(ii)**ABCD is a rectangle. - Prove that a cyclic parallelogram is a rectangle.

**Solve Practice Questions From The Chapter Circles Now**

## FAQs on NCERT Solutions for Class 9 Maths Chapter 10

Here are the frequently asked questions (FAQs) on NCERT Solutions for Class 9 Maths Chapter 10:

**Q1. What can I learn from NCERT Class 9 Maths Chapter 10?**** A.** In this chapter, you will learn about

**circles,**its related terms, and the properties of a circle. Moreover, you will also learn some terms related to circles like the centre of a circle, radius, diameter, arcs, and its types – major arc and minor arc, semicircle, chords, cyclic quadrilaterals, segments, and its two types – major segment and minor segment, etc.

*Q2. Which topics are covered in NCERT Class 9 Maths Chapter 10?*** A**. The topics involved in the NCERT Class 9 Maths Chapter 10 are as follows:

- 10.1: Introduction
- 10.2: Circles and its related terms: A Review
- 10.3: Angle Subtended by a chord at a point
- 10.4: Perpendicular from the Centre to a Chord
- 10.5: Circle through three points
- 10.6: Equal Chords and their distances from the Centre
- 10.7: Angle Subtended by an Arc of a Circle
- 10.8: Cyclic Quadrilaterals
- 10.9: Summary

**Q3. How many exercises are present in NCERT Class 9 Maths Chapter 10?*** A.* The NCERT Class 9 Maths Chapter 10 is divided into 9 sections and 6 exercises. The NCERT Solutions for Class 9 Maths Chapter 10 involves exercise 10.1, exercise 10.2, exercise 10.3, exercise 10.4, exercise 10.5, and exercise 10.6.

*Q4. What is the difference between a chord and a diameter?*** A.** A chord is described as a line segment drawn between any two points in a circle. However, a diameter is drawn at the middle of a circle. It cuts the circle into two halves.

*Q5. Are the NCERT Solutions for Class 9 Maths Chapter 10 easy to understand?** A. *The NCERT Solutions by Embibe will help you in understanding the chapter Circle better. The NCERT Solutions for Class 9 Maths Chapter 10 have been explained in a step by step manner and detailed manner. So that any class 9 student can understand NCERT Solutions for Class 9 Chapter 10.

*Q6. What are the benefits of using NCERT Solutions for Class 9 Maths Chapter 10?*

A. The concepts are explained in simple language in the NCERT Solutions for Class 9 Chapter 10 by Embibe. To boost up your performance in the exam, you can solve free Class 9 Maths Circle questions at Embibe. Also, students can take the CBSE Class 9 Circles Chapter-wise mock test to test their performance. These are some of the benefits of using NCERT Solutions for Class 9 Maths Chapter 10.

*We hope this article on NCERT Solutions for Class 9 Maths Chapter 10 – Circles helps you. If you have any questions, feel free to ask in the comment section below. We will get back to you at the earliest.*