An equilateral triangles ahs a circumradius of `4sqrt(3)` cm. Find its radius ( in cm).

Options

A. `2sqrt(3)`
B. `3sqrt(3)`
C. `sqrt(3)`
D. `(sqrt(3))/(2)`

Explanation

To find the radius of an equilateral triangle given its circumradius, we can use the relationship between the circumradius (R) and the radius (r) of the triangle.

### Step-by-Step Solution:

1. **Understand the relationship between circumradius and radius**:
For an equilateral triangle, the relationship between the circumradius (R) and the radius (r) is given by the formula:
\[ r = \frac{R}{3} \]
where R is the circumradius.

2. **Substitute the given circumradius**:
We are given that the circumradius \( R = 4\sqrt{3} \) cm. We will substitute this value into the formula:
\[ r = \frac{4\sqrt{3}}{3} \]

3. **Calculate the radius**:
Now, we perform the division:
\[ r = \frac{4\sqrt{3}}{3} \text{ cm} \]

4. **Final answer**:
Therefore, the radius of the equilateral triangle is:
\[ r = \frac{4\sqrt{3}}{3} \text{ cm} \]