# What is Circle – Definition, Formula, Properties, & Examples

You are going to learn more about the circles today. We will answer all of your questions such as what is circle, different types of circles, parts of circles, examples of circular-shaped objects in our daily lives, formulae related to circles, properties of circles, and most importantly about “pi”.

### What is Circle?

Circles are two-dimensional round-shaped figure formed by tracing all points in a plane such that they are at an equal distance from a fixed point, center. Look around, can you find something circular in shape? What about the shape of a wheel? A clock? A coin? Round cookies? They are all circular in shape, right?

Definition of Circle

A circle is a two-dimensional geometrical shape. It is a round figure whose boundary is made up of points that are equidistant from a fixed point called the center of the circle. It has 0 vertices and 0 number of edges.

The word circle is derived from the Greek word “kirkos”, which means a hoop or a ring. The radius of the circle is the same from a fixed point in the center.

Examples of Circular Shaped Objects:
1. Coin
2. Bicycle wheels
3. Slice of a lemon
4. Round wall clock
5. Ferris wheel

### Parts of a Circle

The different parts of a circle are diameter, radius, chord, tangent, arc, centre, sector and secant.

1. Radius of the circle (r) –The distance from the centre of the circle to any point on the boundary of the circle is called the radius of the circle. It is denoted by the letter ‘r’ or ‘R’.

2. Diameter of the Circle (d): A line that divides the circle in two equal halves, passes through the center and whose both ends lie on the boundary of the circle is called the diameter of the circle. It is denoted by the letter ‘d’ or ‘D’. The diameter of the circle is 2 times the radius of the circle. Which is why you can also say that d = 2r.

3. Centre of the Circle: A fixed point in the circle

4. Chord of the Circle: Chord is a line segment whose both endpoints touch the boundary of the circle. The Diameter is the longest chord of the circle.

5. Semi Circle: Half the circle is called a semicircle. A semi-circle is a type of circle which is formed when you cut a whole circle into two equal halves.

6. Quarter Circle or Quadrant of a Circle: When you cut the circle into 4 equal parts, each part is known as the quadrant or quarter circle

7. Tangent of a circle: A tangent is a line that touches at exactly one point without entering the circle. The point where the tangent touches the circle is known as the point of tangency. Only one tangent can pass through a point on the circle.

8. Arc of a circle: An arc is the part or portion of the circumference of the circle. We can also say that the circumference of the circle is the full arc of the circle.

9. Sector of a circle: A sector of a circle is the portion of a circle formed by its two radii and an arc of the circle. Have you ever seen a sector of a circle in your real life? Yes, a slice of a pizza is a perfect example of the sector of a circle.

10. Secant of a circle: Remember tangent? The only thing that differentiates secant from tangent is that secant intersects the circle at two different points.

### Circle Properties

Below are the properties of circles:

1. The boundary of the circle is always at equal distance from the center
2. The circle is divided into two equal parts by the diameter of the circle.
3. When two circles have equal radii, they are said to be congruent whereas when two circles have different radii, they are called as similar circles.
4. The diameter of the circle is two times the radius.
5. The longest chord of the circle is its diameter.

What is Pi (π)?

Pi (π) is defined as the ratio of circumference to the diameter of a circle. Pi is denoted by the Greek letter ‘π’. Pi is basically a mathematical constant.

### Calculating the Circumference

The length of the boundary of a circle is called the circumference or perimeter of the circle.It is measured in cm or m.

Calculate the Circumference of Circle –

To derive the formula for calculating the circumference of the circle, let’s remember that π = C/D, where c is the circumference of the circle and d is the diameter. To find C we can rearrange the formula as: C= π x D and thus we got the formula for the circumference of the circle!

You might be thinking that if the circumference of the circle is π x D then why do we write 2πr? It is because the diameter is two times the radius of the circle so the formula for the circumference of the circle can be simply written as C = 2πr

### Calculating a Circle’s Area

Area of the circle is the region enclosed within the perimeter of the circle.

The formula for calculating the area of the circle is

A = π r², where π = 22/7 or 3.14, and r is the radius of the circle.

Learn the Basic Formula of Circles:
1. D= 2 X R
2. C= 2πr
3. A= π r²

Also Learn Here About Rational Number