Parts of a Circle: Definition, Formula, Examples

What Are the Parts of a Circle?

There are many parts of a circle, which include center, radius, diameter, circumference, etc. In this article, we will learn about the circle, the different parts of a circle and their definitions in detail.

Definition of a Circle

In our daily lives, we come across shapes such as clocks, plates, round tables, wheels, coins, etc. These are all round, i.e., circular in shape. A circle is a round two-dimensional plane figure, which is formed by the set of all those points that are at a fixed distance from a fixed point in the same plane. The circle looks similar to the letter “O.”

Based on the shape and position, there are different parts of a circle in geometry that can be listed as center, radius, circumference, diameter, chord, arc, segment, tangent, secant, and sector. It will be easy to identify and label parts of a circle using the diagram shown below.

Circle and Its Parts

Let’s discuss different parts of circles in detail. Identifying parts of a circle becomes easy once you understand the definitions.

Center of a Circle

The fixed point in the plane is called the center of the circle.

Radius of a Circle

The fixed distance from the center to the boundary of the circle is called the radius of the circle. Generally, the radius of a circle is denoted by “r.”

Circumference of a Circle

The total distance measured once around the circle is known as the circumference of the circle.

Circumference of a circle $= 2\pi r$

Where,

$r =$ radius of the circle.

$\pi \simeq 3.14$ or $\frac{22}{7}$ (approx value)

Diameter of a Circle

A line that crosses from the center of the circle starting from one point to the other point of the circumference is called a diameter.

Chord of a Circle

The chord of a circle is a line segment that joins two different points on the circumference of the circle. The diameter is the largest chord of a circle.

Arc of a Circle

A part or segment of the circumference of a circle is called the arc.

Segment of a Circle

A segment of a circle is a part of the circle bounded by a chord and an arc.

Tangent of a Circle

The tangent of a circle is a straight line that touches the circle at a single point.

Sector of a Circle

A sector is a part of a circle that is created by two radii. There are two types of sectors.

Major sector

The sector of the circle that occupies the larger portion is called the major sector.

Minor sector

The sector of the circle that occupies the smaller portion is called the minor sector.

Secant of a Circle

The secant of a circle is the extension of the chord of a circle to the outside of the circle.

Let’s summarize the parts of a circle in one picture!

Regions of Circle

Any closed geometric figure has three regions. Since a circle is also a closed figure, it, too, has three regions. A circle has an inside, an outside, and an “on” because we could be right on the circle. A point can lie in any of these three regions of the circle, namely the Interior region, the exterior region, or on the circle.

Interior Region of the Circle

The region inside the circle is called its interior region and the point that lies in this region is called the interior point. 

The Exterior Region of the Circle

The region outside the circle is called the exterior region of the circle and any point lying outside the circle is said to be in its exterior region. 

On the Circle

Any point on the boundary of the circle is said to be on the circle. 

In this image,

Point A is outside of the circle,

Point B is inside of the circle, and

Point C is on the circle.

Facts

• The word “circle” is derived from the Greek word κρίκος (krikos), meaning “hoop” or “ring.”
• A circle is a curved shape with no edges.
• The diameter is the longest distance between two points on a circle. Alternatively, we can also say that the diameter is the longest chord of the circle.
• The measurement of the full arc of a circle is 360 degrees.
• When we divide the length of the circumference by the length of the diameter, we get 3.141592654 . . ., which is the number $\pi$ (Pi).

Conclusion

In this article, we saw some of the real-life examples of a circle, found out the definition of a circle, and learned about the different parts and regions of a circle. Now, let’s look at some examples and do a few practice questions to better understand the subject.

Solved Examples

1. Find the radius of a circle with a diameter of 12.5 inches.

Solution: 

Given: the radius of the circle $= 12.5$ inches

We know that the diameter of a circle $=$ Radius of circle$ \div 2$

        $= 12.5$ inches$\div 2 = 6.25$ inches.

$\therefore$ Diameter of a circle $=  6.25$ inches.

2. Find the circumference of a coin if its radius is 77 inches.

Solution: 

Given: the radius of the circle $= 77$ inches

We know that circumference $= 2\pi r$

$\Rightarrow $Circumference $= 2\pi r = 2 \times \frac{22}{7} \times 77 = 2 \times 22 \times 11 = 484$ inches.

$\therefore$ Circumference of the circle $=  484$ inches.

3. Find the diameter of a circle if its circumference is 110 feet.

Solution: 

Given: the circumference $= 12.5$ feet

We know that the circumference $= 2\pi r$

$\Rightarrow r =$ Circumference/$2\pi$

$\Rightarrow 2r =$ Circumference/$\pi = \frac{110}{3.14} = 35.03$

$\therefore$Diameter of circle $=  35.03$ feet.

4. Identify the radius, diameter, and chord In the figure given below.

Solution: 

OA, OB, and OC are the radii.

AB is the diameter of a circle.

Since the diameter is the longest chord, AB is also a chord.

Hence, PQ and AB are the chords of the circle.

5. Identify the points and write whether each is the interior or exterior region of the circle or on the circle.

Solution:

The interior points of the circle are C and D.

The exterior points of the circle are A and F.

The points on the circle are B and E.

Practice Problems Parts of a Circle

Frequently Asked Questions Parts of a Circle