Access free live classes and tests on the app
Download
+
Unacademy
  • Goals
    • AFCAT
    • AP EAMCET
    • Bank Exam
    • BPSC
    • CA Foundation
    • CAPF
    • CAT
    • CBSE Class 11
    • CBSE Class 12
    • CDS
    • CLAT
    • CSIR UGC
    • GATE
    • IIT JAM
    • JEE
    • Karnataka CET
    • Karnataka PSC
    • Kerala PSC
    • MHT CET
    • MPPSC
    • NDA
    • NEET PG
    • NEET UG
    • NTA UGC
    • Railway Exam
    • SSC
    • TS EAMCET
    • UPSC
    • WBPSC
Login Join for Free
avtar
  • ProfileProfile
  • Settings Settings
  • Refer your friendsRefer your friends
  • Sign outSign out
  • Terms & conditions
  • •
  • Privacy policy
  • About
  • •
  • Careers
  • •
  • Blog

© 2023 Sorting Hat Technologies Pvt Ltd

  • Introduction to Commission
  • Exam Pattern
  • Syllabus
  • Free Notes
  • Free Classes
  • Free Tests
  • Paper Analysis
  • Study Material
  • Prelims Answer Analysis
BPSC » BPSC Study Materials » Data Analysis » Circle
doubtsolving_bpsc

Circle

A circle is often referred to as the locus of equidistant points drawn from the centre. This article will be your ultimate guide to circles.

Table of Content
  •  

In mathematics or geometry, a circle is a specific type of ellipse with zero eccentricity and two coinciding foci. A circle is often referred to as the locus of equidistant points drawn from the centre. The radius of a circle is the distance between its centre and its outside line. The diameter of a circle is defined as the line that splits it into two equal pieces and is also equal to twice the radius.

A circle is a fundamental two-dimensional form that is defined by its radius. The rings denote the plane’s inner and exterior areas. It is comparable to the line segment type. Consider the line segment curled around till its ends meet. Arrange the loop in such a way that it is perfectly round.

How to Draw a Circle

Here’s how you can draw a circle: 

  • Take an empty piece of paper and make a single mark in the centre of it, naming it point O.
  • Choose a random radius length, such as 3 cm.
  • Maintain the reference zero mark on point O and randomly mark 3 cm away from it in all directions using a ruler.
  • Make as many points as you like away from point O, but they must all be precisely 3 cm apart.
  • After selecting a significant number of points, you may observe that the form begins to resemble a circle, which is just what a circle is.

Parts of a Circle

  • The region bordered by two concentric circles is called an annulus. Essentially, it is a ring-shaped item.
  • An arc is a circle’s linked curve.
  • A sector is a rectangular rectangle defined by two radii and an arc.
  • An area enclosed by a chord and an arc connecting its endpoints is called a segment. It’s worth noting that segments lack a central axis.
  • The centre of a circle is its midway.
  • A chord is a section of a line whose ends are on a circle.
  • Diameter- A line segment that connects the circle’s two ends and is the circle’s greatest chord.
  • A radius is a line segment that connects the circle’s centre to any point on the circle.
  • A secant is a straight line that cuts a circle in half at two places. Additionally, it is referred to as an extended chord.
  • A tangent is a coplanar straight line that intersects the circle at one point.

Radius is the piece of a circle’s circumference that connects the circle’s centre to any point on the circumference. The radius of a circle is indicated by the letters “R” or “r”.

Diameter is a line segment that contains both of the circle’s ends. It is twice the radius’s length, i.e. d = 2r. The radius of a circle is calculated using the diameter as the formula r= d/2.

Circumference of a Circle

A circle’s circumference is defined as the distance around it. ‘Perimeter’ is a technical term which is occasionally used as well, however this is not the case most of the time. It usually refers to the distance between polygons, which are forms composed of straight line segments.

The formula for the circumference of a circle is as follows:

C = 𝜋d = 2𝛱r

Where is 𝜋 = 22/7 or 3.14

Area of Circle Formula

The area of a circle is the volume of space that it occupies.

The formula for calculating the area of a circle is as follows: Area of a circle = 𝜋r2.

Properties of a Circle

Here are the properties of a circle you should know:

  • A circle’s outside line is equidistant from its centre.
  • The diameter of a circle divides it in half.
  • Circles with identical radii are congruent.
  • Circles of varying sizes or radii are comparable.
  • The diameter of a circle is equal to the radius multiplied by two.

Solved Questions

  • Find the circumference and area of a circle whose radius is 42cm. (Take 𝜋=22/7)

Answer: Circumference of the circle will be 2𝜋r = 2 x 22/7 x 42 = 264cm

Area of the circle will be 𝜋r2 = 22/7 x 42 x 42 = 5544cm

  • Find the area of a circle whose circumference is 264cm.

Answer: Circumference of a circle is 2𝜋r which is equal to 264cm in this question.

2𝜋r = 264

2 x 22/7 x r = 264

r = 264 x 7 / 2 x 22

r = 42cm 

Area of the circle will be 𝜋r2 = 22/7 x 422 = 5544cm

Conclusion

To sum it all up:

  • A circle is a closed two-dimensional curve with all points on its surface equidistant from the centre point. 
  • The arc, chord, centre, diameter, radius, tangent, arc, sector and secant are the various components of a circle. 
  • If “r” is the radius of the circle, the area and circumference of the circle are calculated as follows:
  • A circle’s circumference is equal to 2𝜋r units.
  • A circle’s area is equal to 𝜋r2 square units.
faq

Frequently asked questions

Get answers to the most common queries related to the BPSC Examination Preparation.

How will you define the circumference and area of a circle?

Ans. The circle is a 2D shape that has an area and a circumference. The circumference of a circle is sometimes refer...Read full

What is a circle? Explain in detail.

Ans. A circle is a form made up of all points in a plane that are at a constant distance from a given point, the cen...Read full

Explain inscription of circles in other 2D shapes?

Ans.  Each triangle has a unique circle, termed the incircle, that may be in...Read full

What is ‘squaring the circle’

Ans. Squaring the circle is the ancient geometers’ task of building a s...Read full

Ans. The circle is a 2D shape that has an area and a circumference. The circumference of a circle is sometimes referred to as the perimeter, as it is the distance around the circle. The area of a circle is the territory contained within it on a two-dimensional plane.

Ans. A circle is a form made up of all points in a plane that are at a constant distance from a given point, the centre; alternatively, it is the curve drawn out by a point moving in a plane at a constant distance from a given point. The radius is the distance between any two points on a circle and its centre. Typically, the radius must be a positive integer. A circle with radius equal to zero is a degenerate instance.

Ans.  Each triangle has a unique circle, termed the incircle, that may be inscribed in such a way that it is perpendicular to each of the triangle’s three sides. 

A unique circle, termed the circumcircle, may be circumscribed around each triangle so that it passes through each of the triangle’s three vertices.

Tangential polygons, such as tangential quadrilaterals, are any convex polygons inside which a circle tangent to each side of the polygon may be inscribed. Tangential polygons include all regular polygons and triangles.

Ans. Squaring the circle is the ancient geometers’ task of building a square with the same area as a given circle using only a finite number of steps using a compass and straightedge.

In 1882, the job was demonstrated to be impossible due to the Lindemann–Weierstrass theorem, which establishes that pi is a transcendental. Despite its impossibility, math aficionados continue to be fascinated by this subject.

 

Crack BPSC with Unacademy

Get subscription and access unlimited live and recorded courses from India’s best educators


  • Structured syllabus
  • Daily live classes
  • Ask doubts
  • Tests & practice
Learn more

Related articles

Learn more topics related to Data Analysis
Time and Work

The concepts of time and work help figure out how much time and how many people are required to complete a given task.

Time and Distance

In order to calculate the average speed of an item like an automobile over a certain distance, one can divide the distance travelled by the time taken to complete the journey.

Number System

A number system can be characterised as a method of expressing numbers through writing. In this article, we will discuss Indian and international numerical systems.

Mixture and Alligation

With the help of these formulae, you'll be able to answer queries about mixture and alligation with ease.

See all
Access more than

1,770+ courses for BPSC

Get subscription

Related Links

  • Introduction to Commission
  • Exam Calender and Notifications 2022
  • Exam Pattern
  • Syllabus
  • Free Notes
  • Free Classes
  • Free Tests
  • Paper Analysis
Subscribe Now
.
Company Logo

Unacademy is India’s largest online learning platform. Download our apps to start learning


Starting your preparation?

Call us and we will answer all your questions about learning on Unacademy

Call +91 8585858585

Company
About usShikshodayaCareers
we're hiring
BlogsPrivacy PolicyTerms and Conditions
Help & support
User GuidelinesSite MapRefund PolicyTakedown PolicyGrievance Redressal
Products
Learner appLearner appEducator appEducator appParent appParent app
Popular goals
IIT JEEUPSCSSCCSIR UGC NETNEET UG
Trending exams
GATECATCANTA UGC NETBank Exams
Study material
UPSC Study MaterialNEET UG Study MaterialCA Foundation Study MaterialJEE Study MaterialSSC Study Material

© 2023 Sorting Hat Technologies Pvt Ltd

Unacademy
  • Goals
    • AFCAT
    • AP EAMCET
    • Bank Exam
    • BPSC
    • CA Foundation
    • CAPF
    • CAT
    • CBSE Class 11
    • CBSE Class 12
    • CDS
    • CLAT
    • CSIR UGC
    • GATE
    • IIT JAM
    • JEE
    • Karnataka CET
    • Karnataka PSC
    • Kerala PSC
    • MHT CET
    • MPPSC
    • NDA
    • NEET PG
    • NEET UG
    • NTA UGC
    • Railway Exam
    • SSC
    • TS EAMCET
    • UPSC
    • WBPSC

Share via

COPY