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+b` (b) `b+c` `c+a` (d) `a+b+c`

Explanation

To solve the problem, we need to find the value of \(2(r + R)\) in triangle \(ABC\) where \(\angle C = \frac{\pi}{2}\) (90 degrees). Here, \(r\) is the inradius and \(R\) is the circumradius of the triangle.

### Step-by-Step Solution:

1. **Identify the relationship between sides and circumradius:**
In a triangle, the circumradius \(R\) can be expressed as:
\[
R = \frac{c}{2\sin C}
...