Multiple choice

A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of second square is -

  1. 5 : 2

  2. 5 : 4

  3. 4 : 5

  4. 2 : 5
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A Correct answer
Explanation

For a square inscribed in a circle of radius r: diagonal = 2r, so side = 2r/√2 and area = 2r². For a square inscribed in a semicircle of radius r: if the diameter is the base, side = r/√2 and area = r²/2. Ratio of areas = 2r²:(r²/2) = 4:1. The question likely expects the square on diameter configuration.

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