Q34 of 45 Page 12

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.

(CBSE 2013)




Radius (r1) of larger circle = 7 cm


As OD = r2  = 7 cm 

Radius (r2) of smaller circle = cm


Area of smaller circle = π (r2)2


=  x  x 


= cm2


Area of semi-circle ACB = 1/2 Πr12


=  x  x (7)2


= 77 cm2


Area of triangle ABC =  x AB x OC

As AB = OB +  OA

⇒ AB = 7 + 7

⇒ AB = 14 cm


Area of triangle ABC =  x 14 x 7


= 49 cm2


Area of the shaded region


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


= + 77 – 49


= 28 +


= 28 + 38.5


= 66.5 cm2

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