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Question

Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square .


Solution


Let the side of the square inscribed in a square be a units.
Diameter of the circle outside the square = Diagonal of the square = 2a
Radius = 2a2=a2                              
So, the area of the circle circumscribing the square = πa22                         .....(i)
Now, the radius of the circle inscribed in a square = a2
Hence, area of the circle inscribed in a square = πa22                                     .....(ii)
From (i) and (ii)
Area of circle circumscribing a squareArea of circle inscribed in a square=πa22πa22=1214=21
Hence, the required ratio is 2 : 1.
 

Mathematics
RD Sharma (2016)
Standard X

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