If the distance between incenter and one of the excenter of an equilateral triangle is 4 units, then find the inradius of the triangle.

Explanation

To find the inradius of an equilateral triangle given that the distance between the incenter and one of the excenters is 4 units, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The distance between the incenter (I) and one of the excenters (I₁) of a triangle is given by the formula:
\[
II_1 = 4R \sin\left(\frac{A}{2}\right)
...