1989 AIME Problems/Problem 15

Problem

Point $P^{}_{}$ is inside $\triangle ABC^{}_{}$ . Line segments $APD^{}_{}$ , $BPE^{}_{}$ , and $CPF^{}_{}$ are drawn with $D^{}_{}$ on $BC^{}_{}$ , $E^{}_{}$ on $AC^{}_{}$ , and $F{}{}^{}_{}$ on $AB^{}_{}$ (see the figure at right). Given that $AP=6^{}_{}$ , $BP=9^{}_{}$ , $PD=6^{}_{}$ , $PE=3^{}_{}$ , and $CF=20^{}_{}$ , find the area of $\triangle ABC^{}_{}$ .

Solution

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1989 AIME (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Final Problem
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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1989 AIME Problems/Problem 15

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