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A circle is inscribed in a semi-circle as shown:-

 
Soham Agarwal
(@soham)
Estimable Member

A circle is inscribed in a semi-circle as shown:-
CAT Question - Geometry - circles
The radius of the circle possibly is:-

  1. (√2 + 1)/2
  2. √2 − 1/2
  3. 1 − √2
  4. √2 − 1
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Topic starter Posted : 23/03/2021 8:54 pm
Rahul Singh
(@rahul)
Admin

Area of semicircle => (π * 12)/2 = 0.5 π
Area of circle should be less than the area of semicircle:-
Area = π * ((√2 + 1)/2)2 = π/4 * (2 + 1 + 2√2) = (0.75 + √2) * π > 0.5π
Area = π * (√2 − 1/2)2 = π * (2 + 1/4 − √2) = 0.85π > 0.5π
Area = π * (1 − 2√2)2 = π * (1 + 8 − 4√2) = (9 − 5.6)π = 3.4π > 0.5π
Area = π * (√2 − 1)2 =π * (2 + 1 − 2√2)=0.2π

The question is "Find the possible radius of the circle"

Hence, the answer is (√2 − 1).
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Posted : 23/03/2021 8:58 pm
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