2009 AIME I Problems/Problem 5

Problem

Triangle $ABC$ has $AC = 450$ and $BC = 300$ . Points $K$ and $L$ are located on $\overline{AC}$ and $\overline{AB}$ respectively so that $AK = CK$ , and $\overline{CL}$ is the angle bisector of angle $C$ . Let $P$ be the point of intersection of $\overline{BK}$ and $\overline{CL}$ , and let $M$ be the point on line $BK$ for which $K$ is the midpoint of $\overline{PM}$ . If $AM = 180$ , find $LP$ .

Solution

File:A36c841fe89733477edb8466b68743ed0aec6352.png

2009 AIME I (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2009 AIME I Problems/Problem 5

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