CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Triangles. In this problem, it discusses about ratio of areas of equilateral triangle inscribed in circle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 27: Consider equilateral triangle T inscribed in circle C, what is ratio of the areas of T and C? Consider Circle C inscribed in equilateral triangle T, what is ratio of the areas of T and C?

1. 3√3:π , 3√3:16π
2. 3√3:4π , 3√3:π
3. √3:π , 3√3:4π
4. √3:π , √3:16π

Explanatory Answer

Method of solving this CAT Question from Triangles: It is a very basic question.

For any equilateral triangle of side ‘a’
Inradius = \\frac{a}{2√3}\\) and circumradius = \\frac{a}{2√3}\\)

Area of equilateral triangle = \\frac{√3}{4}\\)a²
Area of smaller circle = π * \\frac{a}{2√3}\\) * \\frac{a}{2√3}\\)
Area of larger circle = π * \\frac{a}{√3}\\) * \\frac{a}{√3}\\)

When Equilateral triangle T inscribed in circle C,
Ratio of Areas of T and C :: 3√3:4π

When Circle C inscribed in equilateral triangle T,
Ratio of Areas of T and C :: 3√3:π

The question is "Consider equilateral triangle T inscribed in circle C, what is ratio of the areas of T and C? Consider Circle C inscribed in equilateral triangle T, what is ratio of the areas of T and C? "

Hence, the answer is 3√3:4π , 3√3:π

Choice B is the correct answer.