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Question:

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [Use π=22/7]

63.5 cm2

56.5 cm2

66.5 cm2

60.5 cm2

Solution:

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) × 7 × 14 = 49 cm²
Area of larger circle = πr² = (22/7) × (7)² = 154 cm²
Area of larger semicircle = 154/2 = 77 cm²
Area of smaller circle = πr² = (22/7) × (7/2)² = 77/2 cm²
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 = 133/2 = 66.5 cm²