ln a triangle with sides a, b, c if `r1 gt r2 gt r3` (which are the ex-radii), then

Options

A. `agtbgtc`
B. `altbltc`
C. `a gtb` and `b ltc`
D. `altb` and `bgtc`

Explanation

To solve the problem, we need to analyze the relationship between the ex-radii \( r_1, r_2, r_3 \) of a triangle with sides \( a, b, c \). Given that \( r_1 > r_2 > r_3 \), we will derive the implications of this inequality on the sides of the triangle.

### Step-by-Step Solution:

1. **Understanding Ex-radii**:
The ex-radii \( r_1, r_2, r_3 \) correspond to the sides \( a, b, c \) of the triangle. Specifically:
- \( r_1 = \frac{A}{s - a} \)
- \( r_2 = \frac{A}{s - b} \)
...