Like us!

Have a Look!

WhatsApp Message

Share Link

Area of Segment of Circle

Areas Related to Circles - Concepts

Circumference of Circle

Area of Circle

Arc Length of Sector

Area of Sector

Area of Segment of Circle

Area of Shaded Region

Class - 10th NTSE Subjects

Concept Explanation

Area of Segment of Circle

Area of segment of circle

The portion (or part) of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

Now let us take the case of the area of the segment AQB of a circle with centre O and radius r

Area of the segment AQB = Area of the sector OAQB - Area of $Delta$ OAB

$large Area; of ;sector; OAQB=frac{theta }{360}times pi r^{2}$

$large Area; of Delta ; OAB=frac{1}{2} times base times height = frac{1}{2}times AB times OP$

As angle of the sector and radius is given to us, we will find the value of AB and OP in terms of angle and radius

Now $large Delta OPB$ is a right angled at P

$large therefore sinleft (frac{theta}{2} right )= frac{PB}{OB}=frac{PB}{r}$ $large Rightarrow PB = r;sinleft (frac{theta}{2} right )$

As we that perpendicular to the chord from the centre bisects the chord

$large AB = 2times PB = 2;r;sinleft (frac{theta}{2} right )$

$large and; cosleft (frac{theta}{2} right )= frac{OP}{OB}=frac{OP}{r}$ $large Rightarrow OP = r;cosleft (frac{theta}{2} right )$

$large Area; of Delta ; OAB=frac{1}{2} times 2r; sinleft ( frac{theta}{2} right ) times r ;cosleft ( frac{theta}{2} right )=r^2sinleft ( frac{theta}{2} right ) cosleft ( frac{theta}{2} right )$ $large large Area; of Delta ; OAB=r^2;frac{sin;theta}{2}=frac{1}{2};r^2;sin;theta$

$large Area; of; segment ; OAQB=frac{theta}{360} times pi ;r^2-frac{1}{2}r^2sin;theta$

ILLUSTRATION: O is the centre of the circle, and OA = 28 cm. Find the area of minor segment AQB. $[Take sqrt{2}=1.4.]$

Solution:

$large Area; of; sector; OAQBO=pi times r^{2}times frac{theta }{360}$

$=frac{22}{7}times 28times 28times frac{45}{360}$

$=308;cm^{2}$

$large Area ;of;Delta OAB=frac{1}{2}r^{2};;sin;theta$

$large =frac{1}{2}times 28times 28times sin;45^0$

$large =frac{1}{2}times 28times 28times frac{1}{sqrt{2}}$

$large =196 ;;sqrt{2};;cm^{2}$

Area of segment AQBA = area of sector OAQBO - area of $Delta OAB$

$=(308-196sqrt{2})cm^{2}$

$=(308-274.4)cm^{2}$

$=33.6 ;;cm^{2}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The area of a segment of circle of radius 14 cm if the arc of the segment has a measure of 30 degree is:
A. 3.2 sq cm	B. 4.2 sq cm	C. 2.3 sq cm	D. 5.6 sq cm
Right Option : C
View Explanation

Question : 2

The area of segment of a circle of radius 21 cm if the arc of the segment has a measure of 60 degrees is:
A. 45.27 sq cm	B. 40.27 sq cm	C. 40.8 sq cm	D. None of these
Right Option : B
View Explanation

Question : 3

If O is the centre of a circle of radius r and AB is a chord of the circle at a distance r/2 from O, then $angle BAO=$
A. $60^o$	B. $45^o$	C. $30^o$	D. $15^o$
Right Option : C
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Polynomial I

Polynomials II

Pair of Linear Equations I

Pair of Linear Equations II

Real Numbers I

Real Numbers II

Coordinate Geometry I

Coordinate Geometry II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Introduction to Trigonometry

Some Applications of Trigonometry

Statistics I

Statistics II

Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

Direct and Inverse Variation

Partnership and Mixture

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Class / Course

Students / Parents Reviews [10]

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.

Om Umang

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

View All

Attention !!!!!

Area of Segment of Circle

Area of Segment of Circle

Students / Parents Reviews [10]

Manish Kumar

Hiya Gupta

Archit Segal

Cheshta

Prisha Gupta

Om Umang

Barkha Arora

Shreya Shrivastava

Aman Kumar Shrivastava

Yatharthi Sharma