Difference between revisions of "2000 AIME I Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | In triangle <math>ABC,</math> it is given that angles <math>B</math> and <math>C</math> are congruent. Points <math>P</math> and <math>Q</math> lie on <math>\overline{AC}</math> and <math>\overline{AB},</math> respectively, so that <math>AP = PQ = QB = BC.</math> Angle <math>ACB</math> is <math>r</math> times as large as angle <math>APQ,</math> where <math>r</math> is a positive real number. Find the greatest integer that does not exceed <math>1000r</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2000|n=I|num-b=13|num-a=15}} | |
Revision as of 18:42, 11 November 2007
Problem
In triangle 
it is given that angles 
and 
are congruent. Points 
and 
lie on 
and 
respectively, so that 
Angle 
is 
times as large as angle 
where is a positive real number. Find the greatest integer that does not exceed 
.
Solution
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See also
| 2000 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
