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/Problem 15

Problem

Solution

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