# CAT Practice : Coordinate Geometry

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If you find the relation between the sides of sqaure , triangle and the radius , then you are through!!

## Circle, Square and Triangle

Q.22: A circle inscribed in a square of side 2 has an equilateral triangle inscribed inside it. What is the ratio of areas of the equilateral triangle to that of the square?
1. 9 $\sqrt{3}$ : 16
2. 3 $\sqrt{3}$ : 4
3. 9 $\sqrt{3}$ : 4
4. 3 $\sqrt{3}$ : 16

Choice (D). 3 $\sqrt{3}$ : 16 units

## Detailed Solution

The radius of the circle is 1 unit.
If we considered the side of the equilateral triangle to be ‘a’, the circumradius of an equilateral triangle is R = $\frac{a}{\sqrt{3}}$. a = $\sqrt{3}$.
So, ratio of areas of the equilateral triangle to that of the square is

$\frac{\sqrt{3}}{4} * (\sqrt{3})$2 : (2)2

3 $\frac{\sqrt{3}}{4}$ : 4

3 $\sqrt{3}$ : 16

Correct Answer: 3 $\sqrt{3}$ : 16 units

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## More questions from Geometry Triangles

Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.