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

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

Edited By Safeer PP | Updated on Jul 29, 2022 06:34 PM IST

NCERT Solutions for Class 9 Maths exercise 10.3 - We will first look at the basics definition of the circle then go through the theorems discussed in Class 9 Maths chapter 10 exercise 10.3. A circle is any closed shape with all points connected at an equal distance from the centre. The centre of the circle is any point that is equidistant from any of the circle's boundaries. Radius is a Latin word that means 'ray,' but it refers to the line segment that runs from the circle's centre to its edge. The radius of a circle is defined as any line that starts or ends at the centre of the circle and connects to any point on the circle's border.

NCERT solutions Class 9 Maths exercise 10.3 – This exercise includes some important theorems for examination point of view which are related to chords. We will first see the definition of a chord.

Chord:

Any straight-line segment with both endpoints on the circle's boundary is called a Chord. It literally means 'bowstring' in Latin.

The theorems are:

The perpendicular from a circle's centre to a chord cuts the chord in half.

The line that bisects a chord through the centre of a circle is perpendicular to the chord.

There is only one circle that passes through all three non-collinear points. Circumcircle is the name given to this circle. The Circumcentre and Circumradius are their centre and radius, respectively.

Along with Class 9 Maths ch 9 exercise, 10.3 the following exercises are also present.

## Circles Class 9 Chapter 10 Circles Exercise: 10.3

In (i) we do not have any common point.

In (ii) we have 1 common point.

In (iii) we have 1 common point.

In (iv) we have 2 common points.

The maximum number of common points is 2.

Given : Points P,Q,R lies on circle.

Construction :

1. Join PR and QR

2. Draw perpendicular bisector of PR and QR which intersects at point O.

3. Taking O as centre and OP as radius draw a circle.

4. The circle obtained is required.

Given: Two circles intersect at two points.

To prove: their centres lie on the perpendicular bisector of the common chord.

Construction: Joinpoint P and Q to midpoint M of chord AB.

Proof: AB is a chord of circle C(Q,r) and QM is the bisector of chord AB.

$\therefore PM\perp AB$

Hence, $\angle PMA =90 \degree$

Similarly, AB is a chord of circle(Q,r' ) and QM is the bisector of chord AB.

$\therefore QM\perp AB$

Hence, $\angle QMA =90 \degree$

Now, $\angle QMA +\angle PMA=90 \degree+90 \degree= 180 \degree$

$\angle$ PMA and $\angle$ QMA are forming linear pairs so PMQ is a straight line.

Hence, P and Q lie on the perpendicular bisector of common chord AB.

## More About NCERT Solutions for Class 9 Maths Exercise 10.3

The longest chord is the diameter, and all diameters have the same length, which is two times the radius.

An arc is a segment of a circle that connects two points. Equal chords have equal arcs in a circle.

Diameter refers to a chord that passes through the centre.

Circumference refers to the length of a complete circle.

A circle divides the plane on which it is located into three sections. They are :

(1) Inside the circle, also known as the circle's interior.

(2) Boundary of the circle

(3) The outside of the circle, also known as the circle's exterior.

Also Read| Circles Class 9 Notes

## Benefits of NCERT Solutions for Class 9 Maths Exercise 10.3

• NCERT book Exercise 10.3 Class 9 Maths, is related to the circle and chords.

• NCERT syllabus Class 9 Maths chapter 10 exercise 10.3 introduces us to theorems related to the chords in a circle.

• Understanding the concepts from Class 9 Maths chapter 10 exercise 10.3 will allow us to understand the concepts related to the theorems of chords and circles.

Also, See

## Subject Wise NCERT Exemplar Solutions

1. What is the main concept of NCERT solutions for Class 9 Maths exercise 10.3?

In this exercise, we learn about perpendicular chords that the perpendicular from a circle's centre to a chord cuts the chord in half.

2. What is the perpendicular distance of the chord from the centre if the length of the chord is 8cm and the radius of the circle is 5cm?

The perpendicular distance is 3cm because the perpendicular from a circle's centre to a chord cuts the chord in half. So, the length of hypotenuse i.e. radius is 5cm, length of the base is 4cm hence by the Pythagoras theorem the length of perpendicular is 3cm.

3. What is tangent?

A tangent is a line that intersects a circle in exactly one spot.

4. What is the angle between the radius and the point at which the tangent touches the circle?

The measure of the angle is 90 degrees.

5. What is the maximum number a line can meet a circle?

A line can meet a maximum of two times a circle.

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