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 $m + n. | ||
== Solution == | == Solution == | ||
Revision as of 06:02, 8 October 2007
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Problem
In triangle 
point 
is on 
with 
and 
point 
is on 
with 
and 
and 
and 
intersect at 
Points 
and 
lie on 
so that 
is parallel to 
and 
is parallel to 
It is given that the ratio of the area of triangle 
to the area of triangle 
is 
where 
and 
are relatively prime positive integers. Find $m + n.
Solution
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