## NCERT Solutions for Class 9 Chapter 9 Circles Maths - FREE PDF Download

NCERT Solutions Class 9 Maths Chapter 9 Circles

## FAQs on NCERT Solutions Class 9 Maths Chapter 9 Circles

1. Define Sectors?

The sector is an interior part of a circle which is covered by two radii and one arc of that Circle. These are of two types. The minor sector, which covers less area. The major sector, which covers a large area.

2. Distinguish Between Chord and Diameter?

A chord is a line segment drawn between any two points in the circle. At the same time, the diameter is drawn in the middle of the circle. It cuts the circle into two halves. The radius of a circle is defined as a half part of the diameter.

d = 2r.

3. How are NCERT Solutions for Class 9 Maths Chapter 9 helpful for Class 9 students?

Students who aim to excel in their CBSE Board exams have NCERT textbooks as the best study material at their disposal. In order to fully comprehend the solutions of NCERT textbook problems, students can refer to Vedantu's NCERT Solutions for Class 9 Maths Chapter 9 and download it for free. These solutions offer on point solutions prepared by experts that can help you ace the material in no time.

4. Why should we follow NCERT Solutions for Class 9 Maths Chapter 9?

Here is why you should follow Vedantu's NCERT Solutions:

If you are attempting CBSE Board exams, then a rigorous study of the NCERT syllabus should be your first most priority.

It is equally important to practice the NCERT problems and properly understand their solutions.

Vedantu's NCERT Solutions for Class 9 Maths are curated by Mathematics experts.

The solutions are offered in a direct, logical and understandable way making the concepts easy for students to grasp.

5. What are the basics of Class 9 Maths Chapter 9 Circles?

Chapter 9 Circles talks about the basic concepts and terms related to a circle. The chapter has some important theorems for students to learn. Basic concepts of the chapter include:

Angle Subtended by the Chord at a Point

Perpendicular From the Centre of a Chord

Circles Through Three Points

Chords and Their Distance From the Centre

Angle Subtended by the Area of Circle

Cyclic Quadrilaterals

6. How do I solve the problems of Class 9 Maths Chapter 9 Circles?

Before attempting to solve any problems, it is important that the core concepts are clear in a student’s mind. In order to correctly solve the problems and understand the concepts, students can refer to NCERT Solutions for Class 9 Maths Chapter 9 Circles. These solutions can also be accessed from the Vedantu app. These solutions attempt to solve the problems in the most logical and straightforward way as prepared by Vedantu’s Mathematics expert teachers.

7. What are the most important theorems that come in Class 9 Chapter 9 Circles?

Class 9 Maths Chapter 9 Circles has a lot of theorems. All the theorems mentioned in the chapter are important, and students should practice them well. The main theorems include:

Equal chords of a circle subtend equal angles at the centre.

The perpendicular from the centre of a circle to a chord bisects the chord

Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

In addition to these, all theorems are important and must be practised well.

8. What is the most important theorem in circles for Class 9?

The most important theorem in Class 9 circles is Thales' Theorem (also known as the Angle in a Semi-Circle Theorem). Thales' Theorem is a key concept in Class 9 circles, stating that if you draw a straight line (a diameter) across the middle of a circle and then make an angle from any point on the circle's edge, that angle will always be 90 degrees, or a right angle. Essentially, this theorem helps to explain why any triangle formed with the endpoints of the diameter and a point on the circle is always a right triangle, showcasing a fundamental property of circles in geometry.

9. What is special about circles in Circles Class 9?

In Circles Class 9 , circles are special because they introduce fundamental concepts and properties such as:

Chord properties: Equal chords are equidistant from the centre.

Angle properties: Angles subtended by the same arc are equal, and the angle in a semicircle is a right angle.

Tangent properties: A tangent to a circle is perpendicular to the radius at the point of tangency.

10. How to prove a circle in Ch 9 Maths Class 9?

To prove a circle in Ch 9 Maths Class 9, you can demonstrate that all points on the circle are equidistant from a fixed point called the centre. This involves showing that every line segment drawn from the centre to the circumference (the radius) is of equal length. Additionally, you can verify that any point on the circumference maintains a constant distance from the centre, ensuring that this distance remains the same for all points around the circle. These properties confirm that the shape in question is indeed a circle, as they align with the fundamental definition of a circle in geometry.

11. How many types of circles are there in Ch 9 Maths Class 9?

While there is fundamentally one type of geometric figure called a circle, circles can be categorized based on their relative positions and relationships with each other:

Concentric Circles: Circles that share the same centre but have different radii.

Tangent Circles: Circles that touch each other at exactly one point. They can be internally tangent (one circle inside another) or externally tangent (touching from outside).

Congruent Circles: Circles with the same radius.

12. What is a circle in Class 9 Maths Ch 9?

A circle is essentially a shape where every point along its edge is the exact same distance from a central point. This constant distance is known as the radius. Imagine drawing a perfect loop around a point, making sure every part of the loop is equally far from the centre — that's your circle.

13. What is a chord in a circle Class 9 Maths Ch 9?

A chord in a circle is like a straight road that cuts straight across the circle, touching it at two points on the perimeter. This line doesn't go all the way around; instead, it just stretches from one side of the circle to the other, connecting those two points directly.