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?

- 2√3 : 3π , 3√3 : 4π
- 3√3 : π , 3√3 : 4π
- 3√3 : 2π, 2√3 : π
- √3 : π , √3 : 4π

3√3 : 2π, 2√3 : π

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

Circumradius = a.

Area of regular hexagon = 6 * √3a^{2}/4

Area of smaller circle = π ∗ √3a/2 ∗ √3a/2 = 3πa^{2}/4

Area of larger circle = πa^{2}

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?"**

Choice C is the correct answer.

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