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Question:

In fig., 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 = 14cm, find the area of the shaded region.

Solution:

Area of Shaded region=2×Area of segment BC(or Segment AC)+Area of circle with diameter DO
Since, DO=OC=BO=AO=7cm
∴Area of segment BC=Area of quadrant BOC−Area of ΔBOC=(π×7×7/4)−(1/2×7×7)=14cm²
Area of circle with diameter OD=π×3.5×3.5=38.5cm²
∴Area of Shaded region=(2×14)+38.5=66.5cm²