# The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

Consider the above figure,

From here we can conclude that the portion or the segment below the chord AB is the minor segment and the segment above AB is major segment.

Also we know,

Area of minor segment = Area of sector – Area of ∆AOB eqn1

Now, Area of sector

Where R = radius of the circle and θ = central angle of the sector

Given, R = 7 cm and θ = 90°

Putting these values in the equation 2, we get

Area of sector = 38.5 cm2 eqn3

Area of AOB = 1/2 × base × height

As triangle is isosceles therefore height and base both are 7 cm.

Area of AOB = 1/2×7×7

= 24.5 cm2 eqn4

Putting values of equation 2 and 4 in equation 1 we get

Area of minor segment = 38.5 – 24.5

Area of minor segment = 14 cm2

Area of major segment = πR2 – Area of minor segment eqn5

Put the value of R, and Area of minor segment in equation 5

= π(72) – 14

= 49π - 14

= (22×7) - 14

= 154 - 14

= 140 cm2

Area of minor segment is 14 cm2 and of major segment is 140 cm2.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
RD Sharma | Area of Sector and Segment61 mins
RD Sharma | Area of Sector and Segments25 mins
Throwing the Light on Area of Sector43 mins
Champ Quiz | Area Related with the Circle45 mins
Surface Area and Volume49 mins
Surface Area and Volumes43 mins
Areas Related to Circle36 mins
RD Sharma | Imp Concepts : Surface Area And Volumes43 mins
RD Sharma | Imp. Qs. From Surface Area And Volumes47 mins
Quiz | Surface Area and Volumes42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses