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)