In 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.
In 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.
Radius of larger circle, R = 7 cm
Radius of smaller circle, r = 7/2 cm
Height of ΔBCA = OC = 7 cm
Base of ΔBCA = AB = 14 cm
Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm^{2}
Area of larger circle = πR^{2 }= (22/7) × 7^{2} = 154 cm^{2}
Area of larger semicircle = 154/2 cm^{2 }= 77 cm^{2}
Area of smaller circle = πr^{2} = (22/7) × (7/2) × (7/2) = 77/2 cm^{2}
Area of the shaded region = Area of larger circle – Area of triangle – Area of larger semicircle + Area of smaller circle
Area of the shaded region = (154  49  77 + 77/2) cm^{2}
= 133/2 cm^{2} = 66.5 cm^{2}

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