1992 AIME Problems/Problem 14

Problem

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

Solution

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1992 AIME (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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1992 AIME Problems/Problem 14

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