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Circle- Basics, Definition, Formula, Parts and Properties

The word ‘Circle’ is basically derived from a Latin word ‘circulus’ which means a small ring. A circle is also referred as the locus of the points which are drawn at an equidistant from the center.

As the circle is a 2-D figure, it has an area and perimeter. The perimeter of the circle is also referred to as the circumference of the circle.

In this blog, we will learn the basics, definitions, parts, properties and real-life examples of a circle.

What is a Circle?

A circle can be defined as a two-dimensional figure which is formed by a set of points that are at a fixed distance from a fixed point, namely the center on the plane.

All the points in the plane are equidistant from a given point called “center”.
The fixed distance of the points from the center is called the radius.

The circle formula in the plane is given as:

(a-h)2 + (b-k)2 = r2

where (a,b) are the coordinate points at the plane (h,k) is the coordinate of the center of a circle
and r is the radius of a circle.

Real Life Examples of Circle

There are many objects we see daily in our life that are of circular shape. Some of the real-world examples are:-

1. Wheel
2. Tortilla(chapati)
3. Bottle caps
4. Compact Disks (cd’s)
5. Coin
6. Rings
7. Button

You can notice many such examples of circular objects in our regular life.

Components of Circle

There are various parts or we can say components of a circle that we should know before understanding its properties.

A circle consists of the given components:-

1. Circumference

Circumference is also termed as the perimeter of a circle. It can be defined as the distance covered around the boundary of the circle.

Radius can be defined as the distance from the center of a circle to any point on its boundary. A circle consists of many radii (plural of radius) as it is the distance from the center and touches the boundary of the circle at various points.

3. Diameter

A diameter is a straight line passing through the center that connects two points on the boundary of the circle. The diameter should:

1. pass through the center.
2. Should be straight lines
3. It must touch the boundary of the circle at two distinct(different) points which lie opposite to each other.

4. Chord of a Circle

Chord can be defined as any line segment that touches the circle at two different points on its boundary. The longest chord in a circle is its diameter itself and passes through the center and divides the circle into two equal parts.

Read More : Basic Concept Of Angles In Geometry

5. Tangent

A tangent can be defined as a line that touches the circle at a unique point and lies outside the circle.

6. Secant

Secant can be defined as the line that intersects two points on the circumference or boundary of a circle.

7. Arc of a Circle

An arc of a circle is a curve, that is basically a part or portion of its circumference itself.

8. The segment in a Circle

The area enclosed by the chord and the corresponding arc in a circle is called a segment.

9. The sector of a Circle

The sector of a circle can be defined as the area enclosed by two radii and the corresponding arc in a circle.

Read More : Sum of cubes of n natural numbers

Properties of Circle

1. A circle is a closed two-dimensional shape but is not a polygon.
2. Two circles are said to be congruent if they have an equal radius.
3. Equal chords of the circle are always equidistant from the center of the circle.
4. The diameter of a circle is the longest chord of a circle.
5. The distance from the center of the circle to the diameter is zero.
6. Circles that have different radii are said to be similar.
7. A circle can be inscribed in a square, rectangle, triangle, trapezium, and kite.

Circle Formulas

As the circle is a 2-D figure, it has an area and perimeter to measure it.

1. Perimeter of circle
2. Area of circle

1. Perimeter of a Circle

The perimeter of a circle can be defined as the total length of the boundary of a circle. It is also known as Circumference of the circle.

Circumference = 2πr units.

2. Area of a Circle Formula

The area of a circle can be defined as the amount of space covered by the circle. Area depends on the length of radius of the circle.

Read More : How to find HCF in 10 seconds

Area = πr2 square units.

Solved Examples:-

Example 1:

If the radius of a circular ring is 40 cm. What is the length of the diameter of the ring?

In the given example:-

Radius = r = 40 cm

Diameter of circle = 2 × r.
Hence, the length of the diameter of the circular ring = 2 × 40 = 80 cm.

Example 2:

Find the area of a circle whose radius is 10 m.

In the given example:-
Radius = r = 10 m
Area = πr2
= 3.14 x 10 = 314m2

Example 3:

Find the circumference of a circle whose radius is 6 m.
In the given example:-
Radius = r = 6 m
Circumference = 2πr
= 2 x 3.14 x 6 = 37.68m

Practice Questions:-

1. Find the area of a circle whose circumference is 30 cm.
2. The area of a circle is 176 cm2. Find its radius
3. Find the area and the circumference of a circle whose radius is 5 cm.