Difference between revisions of "2001 AIME I Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | In triangle <math>ABC</math>, <math>AB=13</math>, <math>BC=15</math> and <math>CA=17</math>. Point <math>D</math> is on <math>\overline{AB}</math>, <math>E</math> is on <math>\overline{BC}</math>, and <math>F</math> is on <math>\overline{CA}</math>. Let <math>AD=p\cdot AB</math>, <math>BE=q\cdot BC</math>, and <math>CF=r\cdot CA</math>, where <math>p</math>, <math>q</math>, and <math>r</math> are positive and satisfy <math>p+q+r=2/3</math> and <math>p^2+q^2+r^2=2/5</math>. The ratio of the area of triangle <math>DEF</math> to the area of triangle <math>ABC</math> can be written in the form <math>m/n</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=I|num-b=8|num-a=10}} | |
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Revision as of 00:23, 20 November 2007
Problem
In triangle 
, 
, 
and 
. Point 
is on 
, 
is on 
, and 
is on 
. Let 
, 
, and 
, where 
, 
, and 
are positive and satisfy 
and 
. The ratio of the area of triangle 
to the area of triangle can be written in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
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See also
| 2001 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
