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Question
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.
Solution
Area of minor segment = Area of sector AOBC − Area of right triangle AOB
`= (90°)/(360°) pi(OA)^2-1/2xx"OA"xx"OB"`
`=1/4xx22/7xx(7)^2-1/2xx7xx7`
`=1/4xx22/7xx(7)^2 - 1/2xx7xx7`
= 38.5 - 24.5
= 14 cm2
Area of major segment APB = Area of circle − Area of minor segment
`=(OA)^2 - 14`
`=22/7xx(7)^2-14`
= 154 - 14
= 140 cm2
Hence, the area of major segment is 140 cm2 .
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