In a `DeltaABC, r_(1) + r_(2) + r_(3) -r`=

Options

A. 4R cos A
B. 4R cos B
C. 4R cos C
D. 4R

Explanation

To solve the problem \( r_1 + r_2 + r_3 - r \) in triangle \( ABC \), we will use the formulas for the inradii and circumradius of the triangle. Here’s the step-by-step solution:

### Step 1: Write down the formulas for \( r_1 \), \( r_2 \), \( r_3 \), and \( r \)

The formulas for the inradii \( r_1, r_2, r_3 \) and circumradius \( R \) are given by:

\[
r_1 = 4R \sin\left(\frac{A}{2}\right) \cos\left(\frac{B}{2}\right) \cos\left(\frac{C}{2}\right)
...