Difference between revisions of "2001 AIME I Problems/Problem 4"
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== Problem == | == Problem == | ||
| + | In triangle <math>ABC</math>, angles <math>A</math> and <math>B</math> measure <math>60</math> degrees and <math>45</math> degrees, respectively. The bisector of angle <math>A</math> intersects <math>\overline{BC}</math> at <math>T</math>, and <math>AT=24</math>. The area of triangle <math>ABC</math> can be written in the form <math>a+b\sqrt{c}</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers, and <math>c</math> is not divisible by the square of any prime. Find <math>a+b+c</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=I|num-b=3|num-a=5}} | |
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Revision as of 23:21, 19 November 2007
Problem
In triangle 
, angles 
and 
measure 
degrees and 
degrees, respectively. The bisector of angle intersects 
at 
, and 
. The area of triangle can be written in the form 
, where 
, 
, and 
are positive integers, and is not divisible by the square of any prime. Find 
.
Solution
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See also
| 2001 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
