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.”

Real-life examples of circle

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.

Parts of a circle diagram

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.

Point P as the center of a 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.”

Radius of a circle

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)

Circumference of a circle

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.

Diameter of a circle

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.

Chords of a circle

Arc of a Circle

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

Major and minor arcs of a circle

Segment of a Circle

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

Segment of a circle

Tangent of a Circle

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

Tangent of a circle

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.

Major and minor sectors of a circle

Secant of a Circle

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

Secant of a circle

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

Part of a circle

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. 

Regions of a 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.

  1. 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.

  1. 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.

  1. Identify the radius, diameter, and chord In the figure given below.
Radius, diameter, and chord of a circle

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.

  1. Identify the points and write whether each is the interior or exterior region of the circle or on the circle.
Points on the circle and in the interior and exterior regions of 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

Parts of a Circle: Definition, Formula, Examples

Attend this quiz & Test your knowledge.

1

Which of the following is a part of a circle?

Radius
Tangent
Secant
All of the above.
CorrectIncorrect
Correct answer is: All of the above.
Radius, tangent, and secant all are a part of a circle.
2

Which of the following is not a circle?

The wheel of a bicycle
A car tire
Notebook
Coin
CorrectIncorrect
Correct answer is: Notebook
Notebooks are usually rectangular or square.
3

The total number of chords of a circle is

1
2
3
Infinite
CorrectIncorrect
Correct answer is: Infinite
By joining any two points on the circle, we can draw an infinite (uncountable) numbers of chords of the circle.
4

If a circle has a diameter of 11 inches, what is the length of its longest chord?

5.5 inches
11 inches
22 inches
33 inches
CorrectIncorrect
Correct answer is: 33 inches
The length of its longest chord $=$ diameter of circle $= 11$ inches.
5

A circle with center O has a radius of 8 inches and OP $= 6$ inches. Where does point P lie?

On the circle
In the interior of the circle
In the exterior of the circle
At the center
CorrectIncorrect
Correct answer is: In the interior of the circle
The length of OP is less than the radius of the circle. So point P lies in the interior of the circle.

Frequently Asked Questions Parts of a Circle

The diameter of a circle divides the circular region into two equal parts, each part is called a semicircular region.

Two Semicircles

From two given points, an infinite number of circles can be drawn, as shown in the figure below.

Circles passing through two given points

Circumference of circle $4= 2\pi r$

Area of circle $= \pi r^{2}$, where r is the radius.

Concentric circles are circles having the same center.

An incircle is an inscribed circle of a polygon. It is the largest circle that fits inside the polygon and touches each side of the polygon only at one point. For a triangle, the center of an incircle is the point of intersection of three angle bisectors. 

A circumcircle or circumscribed circle is a circle that passes through each of the three vertices of a triangle. For a triangle, the center of the circumcenter is the point of intersection of the perpendicular bisectors of three sides.