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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.
Solution
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
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