If `I_(1)` is the centre of the escribed circle touching side BC of `!ABC` in which `angleA=60^(@)`, then `I_(1)` A =

Options

A. `r_(1)`
B. `(r_(1))/2`
C. `2r_(1)`
D. none of these

Explanation

To solve the problem, we need to find the distance from the center of the escribed circle \( I_1 \) to vertex \( A \) of triangle \( ABC \), given that \( \angle A = 60^\circ \).

### Step-by-Step Solution:

1. **Understanding the Escribed Circle**: The escribed circle (or excircle) opposite to vertex \( A \) of triangle \( ABC \) has its center denoted as \( I_1 \). The radius of this circle is denoted as \( R_1 \).

2. **Using the Formula**: The distance from the center of the escribed circle \( I_1 \) to vertex \( A \) can be calculated using the formula:
\[
...