1992 AIME Problem 14

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'}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.