In a triangle ABC , let `angleC=(pi)/2`. If r is the in-radius and R is the circum-radius of the triangle , then 2 (r + R) is equal to

Options

A. a+b
B. b+c
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 \(\angle C = \frac{\pi}{2}\). Here, \(r\) is the in-radius and \(R\) is the circum-radius of the triangle.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
Since \(\angle C = \frac{\pi}{2}\), triangle \(ABC\) is a right triangle with \(C\) as the right angle. Let \(a\), \(b\), and \(c\) be the sides opposite to angles \(A\), \(B\), and \(C\) respectively. Here, \(c\) is the hypotenuse.

2. **Circumradius Formula**:
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