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.

Radius (*r*1) of larger circle = 7 cm

Radius (*r*2) of smaller circle = cm

Area of smaller circle = r2^{2}

= * *

= cm^{2}

Area of semi-circle AECFB of larger circle = r1^{2}

= * * (7)^{2}

= 77 cm^{2}

Area of triangle ABC = * AB * OC

= * 14 * 7

= 49 cm^{2}

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 cm^{2}

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