 # Circle Math – Definition, Facts, Types, Properties, Formulas, Examples

A Circle is nothing but an ellipse that has the eccentricity is zero and the two foci are coincident. Also, it can be defined as the locus of all points equidistant from a central point. The circle can divide into two regions named interior and exterior regions. The entire article will let you know the in-depth details of the circle, its properties, parts, etc along with examples. In addition, you will also find circle math formulas and solved problems on the same concept for better understanding.

## Definition of Circle in Geometry

The circle is a closed shape that consists of the set of all the points in the plane that are equidistant from a one-point named a centre. The line that passes through the circle forms the line of reflection symmetry. General Form of the Equation of a Circle in a plane is given by the formula (x-h)2 + (y-k)2 = r2 where (x,y) are the coordinate points, (h,k) is the coordinate of the centre of a circle, and r is the radius of a circle. ## Real-Time Examples of Circle

There are few examples we can see in real life. They are
(i) Ring
(ii) Hula hoop
(iii) Coins
(iv) CD/Disc
(v) Wheels
(vi) Bangles
(vii) Dartboard
(viii) Button

### Parts of Circle

Let us deeply discuss the parts of the circle. The circle has its parts and properties depends on its position in the circle. The different parts of the circle are

#### Arc

The arc is the connected curve of a circle. Or any part of the circumference is also called an arc of the circle.

#### Annulus

The area is bounded by two concentric circles. It looks like a ring-shaped object.

#### Segment

The area is bounded by a chord and an arc. The arc lying between the chord’s endpoints.

#### Sector

The sector is the area bounded by an arc and two radii.

#### Chord

Any line segment that connects two ends of an arc is called a chord. The diameter is considered the longest chord of a circle. #### Centre

The middle point of a circle is known as a Centre. Also, the Centre point is a fixed point and all the points of the closing curve circle are equidistant. #### Diameter

The line segment that passes through the centre and connects both the endpoints on the circle is known as the diameter of the circle. Also, the diameter is the largest chord of the circle. The diameter is twice the length of the radius. d = 2r [Diameter = 2radius]. We can also calculate the radius from the diameter. The radius of the circle formula is r = d/2 [Radius = Diameter/2]. The distance calculated from the centre to any point on the circumference of a circle is known as the radius of that circle. The radius of a circle is denoted by the letter “R” or “r”. Secant – Secant is also known as the extended chord. It is a straight line that cuts the circle at two points.
Tangent – The Tangent is a coplanar straight line that touches the circle at a single point.

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### Circle Math Formulas

Check out the below formulas of the circle. We have given the area and perimeter of the circle formulas here. The circle is measured using two parameters. They are
(i) Area of the circle
(ii) Circumference of a circle

#### Circumference (C)

The curve presents around and closes a circle is called its circumference. The Circumference of the circle is also known as the length of the circle. Also, the circumference is sometimes considered as the perimeter of the circle. A circle circumference formula is
C = πd = 2 π r
Where, π = 3.1415 #### Area (A)

The area of the circle is the amount of space occupied by the circle. The formula for the area of the circle is πr2

### Properties of Circle

The Main Properties of Circles are given below. They are

• Circles that consist of equal radii are congruent to each other.
• Also, circles are that have different radii and different in size are similar.
• The outer line of the circle around the circle is equidistant from the centre of the circle.
• The diameter of the circle is called the largest chord and also it is double the radius.
• The diameter of the circle can divide the circle into two equal parts.

### How to Draw a Circle?

To draw a circle, you need to follow the below procedure.

• Take the empty paper and set a single point on the sheet. Name the middle point as O.
• Then, take some radius for example 4 cm.
• Take the tool named a compass and fix the pencil to the holder on the compass.
• Place one arm at the centre of the circle and take the 4 cm from the centre and draw a circle around the centre point.
• Now, you can get a circle with 4cm of radii.

### Circle Math Problems

Example 1.
Find the area and the circumference of a circle whose radius is 20 cm? (Take the value of π = 3.14)
Solution:
Given that the radius of the circle is 20 cm.
Area of the circle = π r2 = = 3.14  × 202 = 1256 cm2
The area of the circle = 1256 cm2
Circumference, C = 2πr
C= 2 × 3.14 × 20
Circumference= 125.6 cm

Example 2.
Find the area of a circle whose circumference is 15.7 cm.
Solution:
Given that the circumference of the circle is 15.7 cm.
To find the area of a circle, we need to find the radius.
From the circumference, the radius can be calculated:
2 π r = 15.7
(2)(3.14)r = 15.7
r = 15.7 /(2)(3.14)
r=2.5
Therefore, the radius of the circle is 2.5 cm.
The area of a circle is  πr2 square units
Now, substitute the radius value in the area of a circle formula, we get
A = π(2.5)2
A = 3.14 x 6.25
A =  19.625 cm2

Therefore, the area of a circle is 19.625 cm2.

### Frequently Asked Questions on Circles

1. What is a circle?

The circle is a closed shape that has all the points on its surface are equidistant from the centre point.

2. What are the different parts of a circle?

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

3. Write down the formulas of area and circumference of the circle?

The formulas are
Circumference of a Circle = 2πr units
Area of a circle = πr2 square units.

4. What is the radius and diameter of the circle?

The diameter of the circle is the longest chord that is twice the radius. The radius is the line segment that connects the middle point and the point on the circle.

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