In triangle A B C, A^{\prime}, B^{\prime}, and C^{\prime} are on sides \overline{B C}, \overline{A C}, and \overline{A B}, respectively. Given that \overline{A A^{\prime}}, \overline{B B^{\prime}}, and \overline{C C^{\prime}} are concurrent at the point O, and that
\frac{A O}{O A^{\prime}}+\frac{B O}{O B^{\prime}}+\frac{C O}{O C^{\prime}}=92
find the value of
\frac{A O}{O A^{\prime}} \cdot \frac{B O}{O B^{\prime}} \cdot \frac{C O}{O C^{\prime}}