In triangle `A B C ,` let `/_c=pi/2dot` If `r` is the inradius and `R` is circumradius of the triangle, then `2(r+R)` is equal to (a) `a+b` (b) `b+c` (c) `c+a` (d) `a+b+c`

Explanation

To solve the problem, we start with the triangle \( ABC \) where \( \angle C = \frac{\pi}{2} \). We need to find the expression for \( 2(r + R) \) where \( r \) is the inradius and \( R \) is the circumradius of the triangle.

### Step-by-Step Solution:

1. **Identify the circumradius \( R \)**:
In a right triangle, the circumradius \( R \) can be calculated using the formula:
\[
R = \frac{c}{2}
...