NCERT Solutions for Class 9 Maths Chapter 10: Circles - Exercise 10.3

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