Construction of a figure is very important in geometry. Before you draw any figure or shape, such as a circle, you have to know about its basic properties. The construction of different geometrical figures is possible with the help of instruments such as a scale, compass, and a protractor. You know that when drawing, you always use a pencil. Here, we will learn how to draw a circle with the help of geometrical instruments.

It is essential to know that to draw a circle; you need to have certain measurements. The measurements may be about the radius or the diameter. As we go further, we shall learn about the radius and the diameter of a circle and how they help in drawing a circle.

In other words, to draw a circle, we should have the measurements of a given radius or the diameter. These terms define the properties of a circle. Before we start with the construction of a circle, let us discuss the properties of a circle that will help us in drawing the perfect circle.

The properties of a circle are as follows:

Every circle has a radius and a diameter.

The diameter is any straight line segment passing through the centre of the circle.

The diameter joins two opposite points lying on the circumference or boundary of the circle.

The radius of a circle is a straight line or segment that joins the centre of the circle to any point on the circumference or ring of the circle.

The length of the radius is always half of its diameter. Ref Fig.2

Every point on the ring or circumference of a circle is equidistant from the centre.

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We can draw a circle whose radius is given. For the construction of a circle, we need a ruler and a compass. We have to draw a circle with a given radius of 5 cm. Let us start with the following steps.

Place the pointer of the compass at the point 0 cm of a ruler.

Extend the other arm with the pencil to measure 5 cm.

Mark a point O with the pointer on a page of your book. This is the centre of the circle.

Turn the extended pencil-arm of the compass through 360 degrees to draw a full circle.

Points to Remember:

Move the compass in one stroke to reach the point from where you start drawing. Ref Fig 3a.

Hold the pointer of the compass stable so that you get a neat circle. Fig 3b

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You know now that to draw a circle, it is essential to know the following parts of a circle

Radius

Diameter

Chord

Circumference

The distance between the midpoints and the circumference of the circle is the radius. A line segment that passes through the midpoint of the circle and joins any point on the circumference is the diameter. Diameter is two times the size of the radius of a circle. A line segment with its endpoints on the circumference of the circle, not passing through the midpoint is called a chord. Ref fig.4.

It is important to remember that an infinite number of radii, diameters, and chords can be drawn in a circle. They are all congruent or equal, but not the same. All Radii and all diameters of a circle are congruent, but their position in the construction of a circle makes each one different. The circumference of a circle is the outer ring of a circle. It is the distance that goes around a circle i.e., its outer boundary.

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FAQ (Frequently Asked Questions)

Q1. What is the Circumference of a Circle and its Formula?

The circumference is the boundary or the perimeter of a circle. It’s the full distance around a circle. We can find out the length of the circumference of a circle. The circumference is obtained by the formula C = πd where π = 3.14 or 22/7 and d is the diameter of the circle. We can get the circumference by the radius formula too. To find the circumference of a circle with radius 7.5 cm, take π = 3.14. Solution is:

circumference of circle is 2πr = 2 x 3.14 x 7.5cm

= 47.1 cm.

Q2. What are the Properties of a Circle? How to Find the Area of a Circle?

As you know, a circle is round, it has a shape that looks similar to the letter ‘O’. In mathematical terms, circle refers to the boundary or the circumference and all the inner figures. A straight line from the centre of a circle to the edge is called the radius. A straight line that passes from one side of a circle to the other through the centre is called the diameter. Formula to find the area of a circle is = πr^{2} or πd, where r is the radius and d is the diameter, where pi or π = 22/7 or 3.14.