-
A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square is
-
- √3 : 4
- √3 : 8
- 3√3 : 2
- 3√3 : 1
Correct Option: C
Let AB = BC = CA = x units, then
| AD = √ | x² - | = | ||
| 4 | 2 |
| OD = | AD = | = radius of circle | ||
| 3 | 2√3 |
| ⇒ Diagonal of square = 2 × | = | ||
| 2√3 | √3 |
∴ Triangle : Square
| = | x² : | ||
| 4 | 2 × 3 |
| = | : | = 3√3 : 2 | ||
| 2 | 3 |
