-
The ratio of inradius and circumradius of an equilateral triangle is :
-
- 1 : 2
- 2 : 1
- 1 : √2
- √2 : 1
- 1 : 2
Correct Option: A
As per the given in question , we draw a figure of an equilateral triangle with inradius and circumradius 
As we know that ,
| AD = | × Side | |
| 2 |
| ∴ OD = | × AD | |
| √3 |
| OD = | × | = | |||
| 3 | 2 | 2√3 |
| OA = | AD | |
| 3 |
| OA = | × | a = | |||
| 3 | 2 | √3 |
| In-radius = | = | ||
| 2√3 | 2√3 |
| Circum-radius = | = | ||
| √3 | √3 |
| ∴ Required ratio = | : | = 1 : 2 | ||
| 2√3 | √3 |
