Question

A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the area of the minor and major segments.

Answer 1

Let AB be the chord of a circle with centre O and radius 30 cm such that ∠AOB = 60°
Area of the sector OACBO `= (pi"r"^2theta)/360`

`=(3.14xx30xx30xx60/360)"cm"^2`

= 471 cm² 

Area of ΔOAB`=1/2"r"^2"sin"   theta`

 `=(1/2xx30xx30xx"sin "60°)"cm"^2`

= (225 × 1.732) cm² 

= 389.7 cm²

Area of the minor segment = (Area of the sector OACBO) - (Area of ΔOAB)

= (471 - 389.7) cm² 

= 81.3 cm²

Area of the major segment =(Area of the circle) - (Area of minor sregment)

`=|(3.14xx30xx30) - 81.3| "cm"^2` 

= 2744.7 cm²