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A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that d left parenthesis P comma A B right parenthesis less or equal than min(d(P,BC),d(P,DA)) where d(P,AB) is the distance of a point P from line AB. The area of region covered by the moving point P is (sq units)

  1. 4 pi    
  2. 8 pi    
  3. 8 pi minus 16    
  4. 4 pi minus 4    

The correct answer is: 4 pi


    Shaded area is the required region equals fraction numerator pi r to the power of 2 end exponent over denominator 4 end fraction equals fraction numerator pi left parenthesis 4 right parenthesis to the power of 2 end exponent over denominator 4 end fraction equals 4 pi text  sq units. end text

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