In triangle $$ABC^{}_{}$$, $$A'$$, $$B'$$, and $$C'$$ are on the sides $$BC$$, $$AC^{}_{}$$, and $$AB^{}_{}$$, respectively. Given that $$AA'$$, $$BB'$$, and $$CC'$$ are concurrent at the point $$O^{}_{}$$, and that $$\frac{AO^{}_{}}{OA'}+\frac{BO}{OB'}+\frac{CO}{OC'}=92$$, find $$\frac{AO}{OA'}\cdot \frac{BO}{OB'}\cdot \frac{CO}{OC'}$$.

(第一十届AIME1992 第14题)