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Question

The ratio of the area of a square inscribed in a semi-circle to that of the area of a square inscribed in the circle of the same radius is:

A
2:1
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B
2:3
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C
2:5
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D
1:3
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Solution

The correct option is B 2:5
To find:
Area of square IArea of square II=A1A1=s2a2
Let the radius of the circle be r.
Referring to the figure, we get that
s2+s24=r2 [Using Pythagorus theorem]
r=52s
Area of the square I,A1= s2
Now the other circle has same radius as r,
Therefore, The diameter of this circle is 2r=5s
The diameter is same as the length of diagonal of square II.
Let the length of square's side be a, then
a2+a2=5s2
2a2=5s2
s2a2=25
Hence, the ration will be 2:5

588275_103510_ans.png

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