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Difference between revisions of "2002 AIME II Problems/Problem 13"
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== Problem ==
 
== Problem ==
 
In triangle <math>ABC,</math> point <math>D</math> is on <math>\overline{BC}</math> with <math>CD = 2</math> and <math>DB = 5,</math> point <math>E</math> is on <math>\overline{AC}</math> with <math>CE = 1</math> and <math>EA = 32,</math> <math>AB = 8,</math> and <math>\overline{AD}</math> and <math>\overline{BE}</math> intersect at <math>P.</math> Points <math>Q</math> and <math>R</math> lie on <math>\overline{AB}</math> so that <math>\overline{PQ}</math> is parallel to <math>\overline{CA}</math> and <math>\overline{PR}</math> is parallel to <math>\overline{CB}.</math> It is given that the ratio of the area of triangle <math>PQR</math> to the area of triangle <math>ABC</math> is <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>.
 
In triangle <math>ABC,</math> point <math>D</math> is on <math>\overline{BC}</math> with <math>CD = 2</math> and <math>DB = 5,</math> point <math>E</math> is on <math>\overline{AC}</math> with <math>CE = 1</math> and <math>EA = 32,</math> <math>AB = 8,</math> and <math>\overline{AD}</math> and <math>\overline{BE}</math> intersect at <math>P.</math> Points <math>Q</math> and <math>R</math> lie on <math>\overline{AB}</math> so that <math>\overline{PQ}</math> is parallel to <math>\overline{CA}</math> and <math>\overline{PR}</math> is parallel to <math>\overline{CB}.</math> It is given that the ratio of the area of triangle <math>PQR</math> to the area of triangle <math>ABC</math> is <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>.
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== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
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== See also ==
 
== See also ==
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* [[2002 AIME II Problems/Problem 12 | Previous problem]]
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{{AIME box|year=2002|n=II|num-b=12|num-a=14}}
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* [[2002 AIME II Problems/Problem 14 | Next problem]]
 
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* [[2002 AIME II Problems]]
 

Revision as of 13:32, 19 April 2008

Problem

In triangle $ABC,$ point $D$ is on $\overline{BC}$ with $CD = 2$ and $DB = 5,$ point $E$ is on $\overline{AC}$ with $CE = 1$ and $EA = 32,$ $AB = 8,$ and $\overline{AD}$ and $\overline{BE}$ intersect at $P.$ Points $Q$ and $R$ lie on $\overline{AB}$ so that $\overline{PQ}$ is parallel to $\overline{CA}$ and $\overline{PR}$ is parallel to $\overline{CB}.$ It is given that the ratio of the area of triangle $PQR$ to the area of triangle $ABC$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

Solution

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See also

2002 AIME II (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions
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