CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions

The question is from the topic circles. It discusses about a circle inside a semi-circle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. We have to find out the Radius of the circle inscribed inside a semi - circle

Question 37: A circle is inscribed in a semi-circle as shown:-

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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Explanatory Answer

Method of solving this CAT Question from Circles: Let's apply the details in formula directly.

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).

Choice D is the correct answer.