MathematicsIf 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, then find the area of the shaded region.

If 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, then find the area of the shaded region.

Solution:

Area of Shaded region = 2 × Area of segment BC + Area of the circle with diameter DO

Since, DO=OC=BO=AO=7cm

∴ Area of segment BC = Area of quadrant BOC − Area of △ BOC

= $\frac{π}{4} \times 7 \times 7 - \frac{1}{2} \times 7 \times 7 = 14$ cm²

Area of the circle with diameter DO = π × 3.5 × 3.5 = 38.5 cm².

Area of Shaded region = 2 × 14 + 38.5 = 66.5 cm².

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