In any triangle, the minimum value of `r_1r_2r_3//r^3` is equal to (a) 1 (b) 9 (c) 27 (d) none of these

Explanation

To find the minimum value of \( \frac{r_1 r_2 r_3}{r^3} \) in any triangle, we can follow these steps:

### Step 1: Understanding the relationship between the radii
We know that the inradius \( r \) and the exradii \( r_1, r_2, r_3 \) are related to the area \( \Delta \) and the semi-perimeter \( s \) of the triangle. The formulas are:
- \( r = \frac{\Delta}{s} \)
- \( r_1 = \frac{\Delta}{s-a} \)
- \( r_2 = \frac{\Delta}{s-b} \)
- \( r_3 = \frac{\Delta}{s-c} \)
...