Question

Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure. 

Answer 1

Area of minor segment = Area of sector AOBC − Area of right triangle AOB

`=90^circ/360^circ xx pi("OA")^2 - 1/2xx"OA"xx"OB"`

`=1/4xx22/7xx(35)^2 - 1/2xx35xx35`

`= 1/4xx22/7xx(35)^2 - 1/2xx35xx35`

= 962.5 - 612.5

= 350 cm² 

Area of major segment APB = Area of circle − Area of minor segment

= π (OA)² - 350 

`= 22/7xx(35)^2 - 350`

= 3850 - 350

= 3500 cm² 

Hence, the area of major segment is 3500 cm²