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Edited By Safeer PP | Updated on Jul 29, 2022 06:29 PM IST

NCERT Solutions for Class 9 Maths exercise 10.1 is about circles and basic terms related to them. A circle can be characterized as a shut (closed), two-dimensional curved shape, with no pointy vertex, with zero corners such that every point of the circle is equidistant from the fixed centre of the circle. Now we get to know a few terminologies that are related to exercise 10.1 Class 9 Maths. The circumference of a circle is the perimeter of a circle; we can divide the circumference into two parts a major arc and a minor arc. The radius according to NCERT solutions for Class 9 Maths exercise 10.1 is the straight line stretching out from the centre point of a circle to the perimeter or surface, or in simple words, each point on the circumference is at a distance equal to the length of the radius from the centre of the circle. Where the major arc includes the majority portion of the arc and the minor arc includes the minority portion of the arc. The figure below shows the minor arc and the major arc.

Along with Class 9 Maths chapter 10 exercise 10.1, the following exercises are also present.

Fill in the blanks:

** Q1 (i) ** The centre of a circle lies in _____________ of the circle. (exterior/ interior)

** Answer: **

The centre of a circle lies in the interior of the circle.

Fill in the blanks:

** Answer: **

A point, whose distance from the centre of a circle is greater than its radius lies in the exterior of the circle.

Fill in the blanks:

** Q1 (iii) ** The longest chord of a circle is a ___________ of the circle.

** Answer: **

The longest chord of a circle is the diameter of the circle.

Fill in the blanks:

** Q1 (iv) ** An arc is a ________________ when its ends are the ends of a diameter.

** Answer: **

An arc is a semi-circle when its ends are the ends of a diameter.

Fill in the blanks:

** Q1 (v) ** Segment of a circle is the region between an arc and ________________ of the circle.

** Answer: **

A segment of a circle is the region between an arc and chord of the circle.

Fill in the blanks:

** Q1 (vi) ** A circle divides the plane, on which it lies, in _______________ parts.

** Answer: **

A circle divides the plane, on which it lies, into two parts.

Write True or False: Give reasons for your answers.

** Q2 (i) ** Line segment joining the centre to any point on the circle is a radius of the circle.

** Answer: **

True. As line segment joining the centre to any point on the circle is a radius of the circle.

Write True or False: Give reasons for your answers.

** Q2 (ii) ** A circle has only a finite number of equal chords.

** Answer: **

False. As a circle has an infinite number of equal chords.

Write True or False: Give reasons for your answers.

** Q2 (iii) ** If a circle is divided into three equal arcs, each is a major arc.

** Answer: **

False. If a circle is divided into three equal arcs, each arc makes an angle of 120 degrees whereas major arc makes an angle greater than 180 degree at the centre.

Write True or False: Give reasons for your answers.

** Q2 (iv) ** A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

** Answer: **

True.A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

Write True or False: Give reasons for your answers.

** Q2 (v) ** Sector is the region between the chord and its corresponding arc.

** Answer: **

False. As the sector is the region between the radii and arc.

Write True or False: Give reasons for your answers.

** Q2 (vi) ** A circle is a plane figure.

** Answer: **

True. A circle is a plane figure.

NCERT syllabus** Class 9 Maths exercise 10.1 **includes some important concepts like sector and segment of a circle: The sector of a circle is the portion of a circle enclosed by two radii and an arc. Thus, we can divide the sector into two parts the minor and the major sector, where the major sector includes the majority of the area of the circle. A segment of a circle is an area limited by a chord of a circle and the captured arc segment of the circle. A segment with an arc curve under a half-circle is known as a minor portion. A sector with a blocked area than a semi-circle is known as a major segment.

**Also Read| **Circles Class 9 Notes

NCERT book exercise 10.1 Class 9 Maths, is based on Circles and most of the initial terminology of circles.

From Class 9 Maths chapter 10 exercise 10.1 we get to know about segments, sectors and arc of a circle.

Understanding the concepts from Class 9 Maths chapter 10 exercise 10.1 will make the concepts of the next exercise easy to comprehend from our perspective.

**Also, See**

1. What is the core concept of NCERT solutions for Class 9 Maths exercise 10.1?

This exercise deals with all the difficult questions regarding circles and its properties.

2. Define a circle.

A circle can be defined as a closed, two-dimensional curved shape, with zero corners such that every point of the circle is equidistant from the fixed centre of the circle.

3. What is the radius of a circle?

The radius of a circle is the straight line extending from the centre of a circle to the circumference or surface.

4. What is the relation between radius and diameter of a circle?

diameter=2 radius

5. Find the diameter of the circle if the radius is 10 cm?

The relation between the radius and diameter of a circle is:

diameter=2 radius

diameter=20 cm

6. Which segment contains the centre of the circle?

The major segment of the circle contains the centre of the circle whereas the minor segment doesn’t include the centre.

7. Write the formula for circumference of the circle?

The major segment of the circle contains the centre of the circle whereas the minor segment doesn’t include the centre.

Sep 06, 2024

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