CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic regular octagon. It discusses about Regular Hexagon H inscribed in circle C. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. It is a very simple Question.

Question 28: Consider Regular Hexagon H inscribed in circle C, what is ratio of the areas of H and C? Consider Circle C inscribed in Regular Hexagon H, what is ratio of the areas of H and C?

1. 2√3 : 3π , 3√3 : 4π
2. 3√3 : π , 3√3 : 4π
3. 3√3 : 2π, 2√3 : π
4. √3 : π , √3 : 4π

Explanatory Answer

Method of solving this CAT Question from Regular polygon: Go about it by focussing on the radius of the circle or side of the Hexagon.

Inradius = altitude of equilateral triangle of side a = √3a/2

Circumradius = a.
Area of regular hexagon = 6 * √3a²/4
Area of smaller circle = π ∗ √3a/2 ∗ √3a/2 = 3πa²/4
Area of larger circle = πa²
When Hexagon H inscribed in circle C,
Ratio of Areas of H and C :: 3√3 : 2π
When Circle C inscribed in Regular Hexagon H,
Ratio of Areas of H and C :: 2√3 : π

The question is "Consider Regular Hexagon H inscribed in circle C, what is ratio of the areas of H and C? Consider Circle C inscribed in Regular Hexagon H, what is ratio of the areas of H and C?"

Hence, the answer is 3√3 : 2π, 2√3 : π.

Choice C is the correct answer.