If `r=sqrt(8/3)` and `R=35/(4sqrt6)` then the value of sin `X/2`sin `Y/2`sin `Z/2` =

Options

A. `6/35`
B. `4/35`
C. `2/35`
D. `8/35`

Explanation

To solve the problem, we need to find the value of \( \sin \frac{X}{2} \sin \frac{Y}{2} \sin \frac{Z}{2} \) given \( r = \sqrt{\frac{8}{3}} \) and \( R = \frac{35}{4\sqrt{6}} \).

### Step-by-Step Solution

1. **Recall the formula relating \( r \), \( R \), and the sine of half angles**:
\[ r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \]
...