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Question

Question 9
In Fig. 12.27, AB and CD are two diameters of a circle (with center 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.

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Solution

Radius of larger circle, R = 7 cm
Radius of smaller circle, r=72cm
Height of ΔBCA=OC=7 cm
Base of ΔBCA=AB=14 cm
Area of ΔBCA=12×AB×OC=12×7×14=49 cm2
Area of larger circle =πR2=227×72=154cm2
Area of larger semicircle =1542cm2=77 cm2
Area of smaller circle =πR2=227×72×72=772cm2
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 =(1544977+772)cm2
=1332cm2=66.5 cm2

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