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Question
In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [Use Π = 22/7]
Solution
Radius (r1) of larger circle = 7 cm
Radius (r2) of smaller circle = 7/2 cm
Area of smaller circle = `pir_1^2`
`=22/7xx7/2xx7/2`
`= 77/2 cm^2`
Area of semi-circle AECFB of larger circle = `1/2 pir_2^2`
`=1/2xx22/7xx(7)^2`
= 77 cm2
Area of ΔABC = `1/2 xx AB xx OC`
`= 1/2xx14xx7 = 49 cm^2`
Area of the shaded region
= Area of smaller circle + Area of semi-circle AECFB − Area of ΔABC
`= 77/2 + 77 - 49`
`= 28+77/2 = 28 + 38.5 = 66.5 cm^2`
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