Difference between revisions of "1989 AIME Problems/Problem 15"

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== See also ==
 
== See also ==
{{AIME box|year=1989|num-b=14|after=Final Problem}}
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{{AIME box|year=1989|num-b=14|after=Final Question}}

Revision as of 08:50, 15 October 2007

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 $\triangle ABC^{}_{}$.

AIME 1989 Problem 15.png

Solution

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See also

1989 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Final Question
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions