In Fig. 12.27, 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.

Question

Philoid · Accepted Answer

Radius (r1) of larger circle = 7 cm

Radius (r2) of smaller circle = cm

Area of smaller circle = r2²

= * *

= cm²

Area of semi-circle AECFB of larger circle = r1²

= * * (7)²

= 77 cm²

Area of triangle ABC = * AB * OC

= * 14 * 7

= 49 cm²

Area of the shaded region

= Area of smaller circle + Area of semi-circle AECFB - Area of ΔABC

= + 77 – 49

= 28 +

= 28 + 38.5

= 66.5 cm²