MathDB
Triangle Problem

Source: Aime 1992#14

February 17, 2006
AoPSwikigeometrygeometry proposed

Problem Statement

In triangle ABCABC, A′A', B′B', and C′C' are on the sides BCBC, ACAC, and ABAB, respectively. Given that AA′AA', BB′BB', and CC′CC' are concurrent at the point OO, and that AOOA′+BOOB′+COOC′=92,\frac{AO}{OA'}+\frac{BO}{OB'}+\frac{CO}{OC'}=92, find AOOA′⋅BOOB′⋅COOC′.\frac{AO}{OA'}\cdot \frac{BO}{OB'}\cdot \frac{CO}{OC'}.
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