## What is a Circle?

A circle is a two-dimensional shape that is perfectly round. It is defined as the set of all points in a plane that are equidistant from a single point called the **center.** The distance from the center to any point on the circle is called the **radius**, and it is the same for all points on the circle.

A circle is a curved shape that is close all around. It has no corners or edges. It has a centre point. Each point on the boundary of the circle is at an equal distance from the centre.

## Parts of a circle(Radius, Diameter, and Circumference)

### 1. Radius of Circle (r)

The radius of a circle is the distance from the center of the circle to any point on the circle. It is denoted by the letter **“r”.** It is used to calculate the **diameter, circumference, and area**. The length of the radius is also used to define the size of the circle. The radius can be measured in any unit of length, such as meters, centimeters, inches, etc.

### 2. Diameter (d) of Circle

The diameter of a circle is the distance across the circle through its center, passing through two points on the circle. The diameter is twice the length of the radius.

So if the radius of a circle is “r”,

the diameter would be “2r”.

### 3. Circumference of a circle

The circumference of a circle is the distance around its outer edge.

** Circumference of a circle C = 2πr,**

where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

## Area of a circle

The area of a circle is the amount of space inside the circle.

**Area of a circle A = πr ^{2}.**

## Circle Examples in Real Life

Circles have many applications in geometry, physics, engineering, and everyday life. **For example,** they are used in the design of wheels, gears, and pulleys.. Circles also play a key role in trigonometry, where they are used to define angles and to solve problems involving angles, distances, and velocities.

## Solved Examples

**Example 1: Find the area of a circle with radius 5 cm.**

**Solution**:

The formula for the area of a circle is A = πr^{2}.

Substituting the given value of the radius, we get:

A = π(5 cm)^{2}

area of a circle A = 25π cm^{2}

**Example 2: Find the circumference of a circle with diameter 10 meters.**

**Solution:**

The formula for the circumference of a circle is C = πd, where d is the diameter.

Substituting the given value of the diameter, we get:

C = π(10 m)

C = 10π m

Therefore, the circumference of the circle is 10π meters.