In a triangle , if `r_(1) = 2r_(2) = 3r_(3)`, then `a/b` + `b/c` +` c/a` is equal to

Options

A. `75/60`
B. `155/60`
C. `176/60`
D. `191/60`

Explanation

To solve the problem, we start with the given relationship between the inradii of the triangle:

**Step 1: Set up the relationship between the inradii.**
Given that \( r_1 = 2r_2 = 3r_3 \), we can express the inradii in terms of a common variable \( k \):
- Let \( r_3 = k \)
- Then \( r_2 = \frac{3}{2}k \)
- And \( r_1 = 2r_2 = 3k \)

...