In an equilateral triangle the in-radius and the circum-radius are connected by

Options

A. r=4R
B. `r=R/2`
C. `r=R/3`
D. none of these

Explanation

To find the relationship between the in-radius (r) and the circum-radius (R) of an equilateral triangle, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Triangle**:
Let the side length of the equilateral triangle be \( a \). In an equilateral triangle, all sides are equal.

2. **Calculating the Area (Δ)**:
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