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]

Answer 1

Radius (r₁) of larger circle = 7 cm

Radius (r₂) of smaller circle =7/2 cm

Area of smaller circle =  πr₁² 

=22/7 x 7/2 x 7/2

=77/2 cm² 

Area of semi-circle AECFB of larger circle = 1/2  π  r₂²

= 1/2 x 22/7 x 7 x 7

= 77 cm²

Area of ΔABC = 1/2 x AB x OC

= 1/2 x 14 x 7

=49 cm²

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 cm²