Circles: Meaning, Formulas and How to Draw with Examples
Depanjan Chowdhury
| Updated: Apr 20, 2021 15:48 IST
A circle in maths or geometry is a 2D Geometric Shape, that can be defined as a locus of points that is equidistant from a fixed point known as the center for that circle. You can simply define a circle in maths as a round-shaped figure with no corners or edges. This article will make you familiar with the parts of a circle in mathematics, and its various types, followed by the different formulas for area, circumference, radius, centre and more with properties and solved examples.
Circle Definition
The circle in maths can be represented as a closed, two-dimensional curved figure. Or we can even define it as the collection of the points sketched at an equal length from the centre. The fixed distance from the centre to the circumference is the radius and the diameter is the line that passes through the centre and connects two points on the circumference.
Circle Shaped Objects
We come across several objects in real life that is circular shaped. Some examples of circle-shaped objects are wheels of a vehicle, coins, fry pans, drums, bangles, circular plates, CDs, buttons, hula hoops, rings, dinner plates, discs, wall clocks, ferris wheels etc. Several such patterns can be observed in our day to day life.
How to Draw a Circle?
Let us now understand how to draw a circle using different methods:
Sketching a Circle using a Compass
You can draw a circle using a compass with the help of the below steps:
Step 1: Using a scale choose a particular measure i.e. the radius for the circle. Let us say r=3.5cm.
Step 2: Now measure the same radius using the compass as shown in the below image.
Step 3: Next, place the sharp point of the compass on the paper or drawing sheet and rotate it from the pencil side to draw the circle.
Step 4: The obtained figure is the circle with the sharp point as the centre which is kept fixed. Avoid moving the compass while drawing the circle.
Sketching a Circle Using a Protractor
Sketch a circle using a protractor with the help of the below steps:
Step 1: Take a protractor and place it on the paper where you want to draw the circle.
Step 2: Now, trace the circumference of the protractor this will provide you with the semi-circle.
Step 3: Now rotate the protractor and draw the other half to get a complete circle.
The only difference is that here you will get the circle with a fixed radius only. However, using a compass you can circle with multiple radii.
Sketching a Circle Using a String and Pencil
You can also sketch a circle using a string and pencil with the help of the below steps:
Step 1: Take a string or thread and measure a particular distance that will be the radius.
Step 2: Now tie a pencil to one end of the string. Next, hold one end of the string down on the paper and move the pencil all around the string.
Step 3: The obtained figure is the circle of the required radius.
Parts of Circle
A circle has different parts depending on its forms and properties. The different parts of a circle are as follows:
- Centre: The center of a circle is defined as the midpoint of a given circle.
- Radius: A line segment joining the center of a circle to any location on the circle itself is called the radius of a circle.
- Diameter: A line segment whose both endpoints are on the circle and is the largest chord of the circle is called the diameter of a circle.
- Annulus: The area bounded by two concentric circles is called the annulus. It resembles a ring-shaped object as shown in the image.
- Arc: An arc of a circle is related to a curve, which is a section/portion of its circumference.
- Sector: The sector of a circle is the area circumscribed by two radii and the corresponding arc in a circle. There are two types of sectors; minor and major.
- Segment: The area contained by the chord and the corresponding arc of a circle is a segment. The two types of segments are minor and major segments. It should be noted that segments do not include the center.
- Chord: A chord of a circle is any line segment meeting the circle at two distinct points on its circumference.
- Secant: A straight line crossing the circle at two points on the circumference is a secant.
- Tangent: A coplanar straight line that touches the circle at a single unique point is called the tangent.
So far we have gone through the basic concepts of a circle, now we shall see how to draw a circle. Also,
Circle Formulas
In the previous header, we learnt the various parts and how to draw a circle. Let us now understand the different related formulas along with the definition.
| Term | Definition | Formula |
| Circumference of a circle | The circumference of a circle is the distance around the given circle. | \(2\pi r \), where r is the radius. |
| Area of a circle | The area of a circle is the region involved by the circle in a 2D plane. | \(\pi r^{2 }\), when radius(r) is given. \(\frac{\pi d^2}{4}\), when diameter (d) is given. |
| Radius of a Circle | The radius of a circle is the distance measured from the centre to any point on the circumference of the circle. | \(\frac{\text{d}}{2}\), where d is the diameter. |
| Equation of a Circle | The equation of a circle depicts the position of a circle in a Cartesian plane. | \((x−a)^2+(y−b)^2=r^2\) |
| Chord of a Circle | A line segment that connects two points on the circumference of the circle is said to be the chord of the given circle. | Chord Length=\(2\times\sqrt{\left(r^2−d^2\right)}\) |
| Centre of a Circle | The centre of a circle is a location inside the circle which is equivalent to all the locations on the circumference. | For the below equation (a, b) denotes the coordinates of the center. \((x−a)^2+(y−b)^2=r^2\) |
Types of Circles
The different types of circles are as follows:
| Type of Circles | Definition | Diagram |
| Concentric Circles | There are a number of circles one inside the other. All these circles are of varying sizes and have a distinct radius but have a common centre. Such circles are called Concentric Circles. |  |
| Orthogonal Circles | When two circles cut each other at right angles, they are termed as orthogonal circles. |  |
| Congruent circles | Circles that have the same radius/diameter but distinct centres are Congruent, they are termed congruent circles |  |
| Intersecting Circles | When two circles meet at two points or one point, then they are called intersecting circles. |  |
Learn about the general equation of a circle in the linked article.
Properties of Circles
Some of the important properties of circles are as follows:
- The circle’s diameter divides it into two equal sections.
- Circles which possess equal radii or diameters are congruent to one another.
- The diameter of the circle is the longest chord and is twice the radius.
- Equal chords are always at an equal distance from the center of the circle.
- The perpendicular bisector of a chord crosses through the center of the circle.
- When two circles meet, the line joining the intersecting points will be perpendicular to the line joining their center points.
- Circles that are different in measurement or have different radii/ diameters are similar.
- The radius is a perpendicular bisector of the chord of a circle.
- The angle between the radius and the tangent is always 90 degrees.
- Two tangents are identical if they have a common point of origin.
- The radii of equal circles are equal and have equal areas and circumferences.
- The distance between the longest chord(diameter) and the center of a circle is zero.
Check the details of the Pie Chart here.
Solved Example of Circles
With all the knowledge of the formula, definition and properties of circles, let us practise some examples to understand these concepts even more clearly.
Solved Example 1: The circumference of a roller is 450cm. Determine the radius of the roller.
Solution: Circumference of the roller=450cm
Circumference of a circle=\(2\pi r\)
C=450=\(2\times\frac{22}{7}\times r\)
r=71.590 cm
If you have mastered the concepts of circles, you can learn about Triangles here.
Solved Example 2: Find the circumference of a circle disk whose diameter is 28 cm.
Solution:
Diameter of the circle=28 cm.
Circumference of the Circle=\(\pi D\) =\(\frac{22}{7}\times28\ \text{cm}=88\ \text{cm}\)
Solved Example 3: Arun wants to decorate a circular portion of the walls with a wall sticker. If the radius of the circular portion is 70 cm, find the portion of the wall sticker needed to cover the circular surface.
Solution:
Given: r = 70 cm,
Using the formula of area = \(\pi r^{2 }\)
⇒ A =\(\frac{22}{7}\times70\ \times70=15400\text{ cm}\).
The portion of the wall sticker needed to cover the circular surface=15400 cm.
This article focuses on formula-based concepts as this is the current demand for competitive examinations. For more such free theoretical and mathematical concepts, regarding maths and various topics visit our Testbook app.
| If you are checking the Circles article, also check the related maths articles in the table below: | |
| Triangles | Matrices |
| Interest | Sets |
| Comparison of Quantity | Rolles Theorem and Lagranges Mean Value Theorem |
Circles FAQs
Q.1 What is a circle?
Ans.1 A circle in maths is a round-shaped figure with no corners or edges.
Q.2 What are the different types of circles?
Ans.2 The different types of circles are; concentric, orthogonal, congruent and intersecting circles.
Q.3 Is a circle a ball?
Ans.3 The circle is a 2D figure, however, a ball is a 3D object, hence it is not a circle.
Q.4 Given an example of a circle-shaped object?
Ans.4 Music drums, bangles, and circular plates are some examples of a circle-shaped objects.
Q.5 Is a circle the same as an ellipse?
Ans.5 A circle is a special case of an ellipse with both the focus on the same point.
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