NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.3 (Ex 10.3)

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NCERT Solutions for Class 9 Ma...

NCERT Solutions for Class 9 Maths Chapter 10 Circles (Ex 10.3) Exercise 10.3

The students studying in the CBSE board and studying the NCERT Solutions are required to practise from Class 9 Maths Chapter 10 Exercise 10.3 by Vedantu which deals with circles. NCERT Solutions for Class 9 Maths Chapter 10 Circles are studied in a separate chapter that belongs to the stream of mathematics known as mensuration. It is one of the most scoring parts of Mathematics but the students need to have a clear knowledge of the formulas and their applications while solving the numerical problems of Ex 10.3 Class 9 Maths. As a student prepares for the 10th standard boards of CBSE they need to get access to the NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.3 PDF which is available for download as well. Students can also avail of NCERT Solutions Class 9 Science from our website.

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Exercise 10.3

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

Ans: Consider the following pair of circles.

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The above two circles don’t intersect each other at any point. Therefore, they don’t have any point in common.

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The above two circles touch each other at \[Y\] . i.e., only at one point. Therefore, the circles have $1$ point in common.

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The above circles touch each other at $1$ point $X$ only. Therefore, the circles have $1$ point in common.

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These two circles intersect each other at the points $G$ and $H$ . Therefore, these two circles have two points in common. It can be observed that the circles touches maximum of $2$ points in common. Consider the situation in which two congruent circles overlap on each other. This situation can be referred to as if we draw the circle two times.

2. Suppose you are given a circle. Give a construction to find its centre.

Ans: Find the centre of the circle by using the steps

Step 1: We take the given circle.

Step 2: We take any \[2\] different chords $AB$ and $CD$ of the given circle and draw the perpendicular bisectors of these chords of the circle.

Step 3: Let these perpendicular bisectors of the given circle meets at the point $O$ . Hence, $O$ is the centre of the given circle.

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3. If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

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Ans: Consider two circles centered at point $O$ and $O'$ , intersecting each other at point $A$ and $B$ respectively.

Join $AB$ . $AB$ is the chord of the given circle centered at the point $O$ . Therefore, the perpendicular bisector of $AB$ will pass through $O$ .

Again, we see that $AB$ is also the chord of the circle centered at $O'$ . Therefore, the perpendicular bisector of $AB$ will also pass through $O'$ .

It is clear that the centre of the given circle lies on the perpendicular bisector of the common chord.

NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.3 - Free PDF Download

Basic Facts about Circles

If you are currently studying in class 9, it is crucial for you to understand the basic concepts of circles. All facts related to circles are given here in details:

Centre: All circles drawn on paper have a centre. Generally, we have to draw a circle with respect to the centre. The centre, if graphically represented acts as the origin. You can draw a circle with a compass.

Radius: A straight line starting from the centre and meeting the circumference of the circle is known as its radius. If you are drawing a circle, you must measure the radius with the help of a compass.

Diameter: The exact double of the radius can be simply called the diameter. According to the concept, the largest chord that you can cut on a circle is known as diameter.

Circumference: The circular line that makes the shape of a circle is known as the circumference. If you denote the circle in a 2D diagram on the paper, the circumference can act as the surface of the circle.

Chord: Any line that meets two points on the circumference of the circle is known as the chord of the circle. A tangent is also a type of chord that meets only one point of the circle.

When you consider the problems, the only way you can solve them is by knowing about all these and applying the right formulas. You can know about the formulas on educational sites like Vedantu and Maths Ncert Solutions Class 9 Chapter 10 Exercise 10.3. However, you need to be strict about practising the sums regularly. This can help you to recognize a sum by seeing the diagram or going the question. The NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.3 can help you to understand every sum in the exercise.

How NCERT Solutions Can Help

There are many ways by which the maths NCERT Solutions Class 9 Chapter 10 Exercise 10.3 can help you. You should always check for the solutions as it can make your practice session interesting. Here are some points worth remembering:

Benefits of Solving from NCERT Solutions Class 9 Chapter 10 Exercise 10.3

Clears Concepts

The solutions of the NCERT Maths Chapter 10 are made in such a way that all your doubts can be cleared. All you need to do is to apply the right concept at the right place. Avoid making any mistake in case of the formulas as it can turn the sum in the wrong direction.

Boosts Confidence and Speed

If you get access to NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.3, expect your speed and confidence and speed to increase a lot. You should always go for repeated practice sessions for each of the sums on circles.

Solving Unique Problems

All the sums in the exercise have some uniqueness in them. Solving all the sums in the exercise, you will acquire the ability to identify a sum and solve it quickly. The solutions make sure your concept is clear and it can help you to solve unseen sums that you might not be familiar with.

Best for Competitive Exams

When it comes to the chapter on circles, you should know that different competitive examinations include this chapter in the syllabus. Accessing solutions can be an excellent approach for you. As a student of class 9, you can develop an interest in Mathematics if you have the solutions. Moreover, you can develop a concept of the circle shape which can help you with physics and the sums related to it. The solutions are mostly free and you can download them from authentic sites.

You can also refer to NCERT Solutions for Class 9 Maths Circles' other exercises from the links given below.

Exercise 10.1 - Introduction

Exercise 10.2 - Circles and Its Related Terms: A Review

Exercise 10.3 - Angle Subtended by a Chord at a Point

Exercise 10.4 - Perpendicular from the Centre to a Chord

Exercise 10.5 - Circle through Three Points

Exercise 10.6 - Equal Chords and Their Distances from the Centre

FAQs (Frequently Asked Questions)

1. Why are NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.3 needed?

The NCERT Maths Solutions for Class 9 Exercise 10 are needed for the students who desire to be in a leading position in the examination. Moreover, it can be the best for the students who are weak in mathematics and need time and good backup to learn the concepts. Moreover, as a student of class 9, you might need the solution to explore the field of mensuration in an in-depth manner. The best you can do is visit the site of Vedantu and look for the solutions on the site. All you have to do is search for the right solution papers according to your need. You can download the question papers for free and store them in the PDF format.

2. What is the correct approach for doing the sums on circles?

The right approach to do the sums on circles is to know the basic definitions of circles and know the difference between a circle and a sphere. You will have to know the formulas and the abbreviations to solve every sum from this chapter. The best you can do is to refer to the solutions available on the educational websites, Always check the syllabus and the sums present in the solution paper for making the correct match. If you find commonality, consider the solution paper to be relevant. Once you download the right solution paper, you can start solving the sums on a regular basis.

3. Is Chapter 10 Circles an easy chapter to follow?

Chapter 10 Circles might come across as intimidating to some students due to the large number of theorems mentioned in the chapter. However, students must understand that the fundamentals of the chapter are not as complicated. Once they get a hang of the core concepts of Chapter 10, the chapter should not be hard at all. Students should practice the theorems and apply the basic concept to the exercises.

4. I find understanding Circles hard. How should I overcome this?

Firstly, you do not need to get scared of any chapter in Mathematics. It is a subject that requires two things:

Clarity of concepts.
Lots of practice and revision.

After concepts are clear, students can apply these concepts to the textbook problems and easily solve them. They can also refer to Vedantu’s Solutions to practice additional questions. In addition to this, they should solve as many sample papers as they can. This will give you an idea of what sort of questions you will encounter during your exam.

5. How much practice is required to master Chapter 10 Circles?

Mathematics is a subject that requires a great deal of practice. Hence, students should be clear on the concepts from the beginning of the academic year, so that they can get a lot of revision and practice time for this particular subject. They should devote at least 1-1.5 hours on a daily basis dedicated only to Mathematics. The more practice they do regularly, the easier things will be by the end of the academic year.

6. Where can I find solutions for Exercise 10.3?

Vedantu’s NCERT Solutions to Class 9 Mathematics textbooks are prepared as per CBSE guidelines and are ideal to ace the CBSE exams. These chapter-wise solutions are prepared separately for each exercise in the NCERT textbook. This makes it easier for students to find the solutions to the particular exercise that they are looking for. You can access Vedantu’s Solutions for Exercise 10.3 from the page NCERT Solutions for Class 9 Maths Chapter 10. These solutions are available free of cost on the Vedantu app as well.

7. What important concepts is Exercise 10.3 based on?

To solve questions from Exercise 10.3 students must be clear on the following concepts:

The perpendicular from the centre of a circle to a chord bisects the chord.
The line that is drawn through the centre of a circle to bisect a chord, is perpendicular to the chord.
There is one and only one circle passing through three given non-collinear points.

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