Problem

The key is recognizing that $r_1, r_2, r_3$ are the exradii opposite to vertices $A, B, C$ respectively, and expressing them in terms of the semiperimeter $s$ and area $\Delta$. Each exradius has the form $r_i = \frac{\Delta}{s - a_i}$, so ratios like $\frac{r_1}{r_2}$ simplify to expressions involving the side lengths. Expanding the given equation and using these relationships will reveal a constraint on the sides that characterizes a specific triangle type.

The key is recognizing that $r_1, r_2, r_3$ are the exradii opposite to vertices $A, B, C$ respectively, and expressing them in terms of the semiperimeter $s$ and area $\Delta$. Each exradius has the form $r_i = \frac{\Delta}{s - a_i}$, so ratios like $\frac{r_1}{r_2}$ simplify to expressions involving the side lengths. Expanding the given equation and using these relationships will reveal a constraint on the sides that characterizes a specific triangle type.