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Cevians in a triangle

Source: 2009 AIME I #5

March 18, 2009

AMCAIMEgeometryparallelogramratioangle bisectorsimilar triangles

Problem Statement

Triangle

ABC

has AC \equal{} 450 and BC \equal{} 300. Points

K

and

L

are located on

\overline{AC}

and

\overline{AB}

respectively so that AK \equal{} 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 \equal{} 180, find

LP

.

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