Maharashtra Board Class 5 Maths Part One Chapter 7 Circles PDF Download

Circles

Radius, Chord And Diameter

The line joining the centre of the circle to any point on the circle is called a radius of the circle.

In the diagram, P is the centre of the circle while M is a point on the circle. PM is a radius of the circle.

A circle has many radii. They are all of the same length.

A line joining any two points on a circle is called a chord.

In the diagram, M and N are two points on the circle. Line MN is a chord of the circle.

A chord passing through the centre of the circle is called a diameter.

In the diagram, chord AB passes through the centre P. Therefore, chord AB is also a diameter of the circle.

A circle has many chords and diameters.

The centre of the circle below is O. There are other points and lines given in the diagram. Find the radii, chords and diameters in the diagram and write their names in the box provided.

Teacher's Note

A radius is like a stick from the middle of a circle to its edge. A diameter is like a stick that goes all the way across the circle through the middle. Just like measuring from the center of a round roti to its edge, that is the radius.

Exam Trick

Remember: Diameter = 2 times Radius. So if radius is 3 cm, diameter is always 6 cm. The diameter always passes through the center of the circle.

Points to Remember

Radius is a line from the center to any point on the circle.
Diameter is a chord that passes through the center.
All radii of a circle are equal in length.
All diameters of a circle are equal in length.
Diameter is always twice the radius.

Drawing A Circle

We use a compass to draw a circle. One arm of the compass has a metal point while the other arm has a place to fix a pencil. A pencil of a suitable length is fixed to the compass.

How To Draw A Circle Using A Compass

First fix the pencil to the compass. Align the metal tip of the compass with the pencil point as shown in the picture on the right.

Take a convenient distance between the pencil point and the metal tip.

Take any point on a piece of paper.

Hold the metal tip steady on the chosen point and turn the pencil point around it on the sheet of paper. The shape created by the pencil point will be a circle.

The point at which the metal tip of the compass is held is the centre of the circle. In this diagram, C is the centre of the circle.

To draw a circle of a given radius, a distance equal to the radius is kept between the pencil point and the metal tip of the compass. In the accompanying diagram, this distance is 3 cm. Therefore, the radius of the circle drawn using this distance is 3 cm.

Problem Set 28

Draw circles with the radii given below.

2 cm

4 cm

3 cm

Draw a circle of any radius. Show one diameter, one radius and one chord on that circle.

Teacher's Note

A compass is a special tool we use to draw circles. It has a sharp metal point and a pencil. You hold the metal point at the center and rotate the pencil around it. This is just like spinning a rope with a stone at the end.

Exam Trick

When using a compass, always keep the metal point steady at the center. Do not move it or your circle will not be round. Practice drawing circles of different sizes to become good at it.

Points to Remember

A compass has a metal point and a pencil holder.
The metal point marks the center of the circle.
The distance between the metal point and pencil is the radius.
Turn the compass slowly and smoothly to draw a perfect circle.
Always keep the metal point steady while drawing.

Relationship Between Radius And Diameter

Study the circle given alongside. Think over the following questions.

Which are the radii in the circle?

How many radii make up diameter AB?

If the length of one radius is 3 cm, what is the length of the diameter?

How long is the diameter as compared to the radius?

The diameter of a circle is twice the length of its radius.

If another diameter CD is drawn on the same circle, will its length be the same as that of AB?

All the diameters of a circle are of the same length.

Measure the diameters and radii of the circles given below with a ruler and verify the relationship between their lengths.

Draw a circle on a piece of paper and cut it out.

Name the centre of the circle P.

Draw the diameter of the circle and name it AB. Note that PA and PB are radii of the circle.

Fold the circular paper along AB as shown in the picture.

Fold the paper at P in such a way that point B will fall on point A. Radius PB falls exactly on radius PA. In other words, they coincide.

From this, we can see that every radius of a circle is half the length of its diameter.

Problem Set 29

If the radius of a circle is 5 cm, what will its diameter be?

If the diameter of a circle is 6 cm, what will its radius be?

Teacher's Note

The relationship between radius and diameter is very important. Diameter is always 2 times the radius. If you know one, you can easily find the other. It is like knowing the length of one side of a square helps you find the perimeter.

Exam Trick

Remember this formula: Diameter = 2 × Radius, so Radius = Diameter ÷ 2. You can solve any problem about circles using this simple rule.

Points to Remember

Diameter equals 2 times the radius.
Radius equals half the diameter.
All radii of a circle are equal.
All diameters of a circle are equal.
If radius is 5 cm, diameter is 10 cm.

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