Difference between revisions of "2012 AIME I Problems/Problem 12"
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==Problem 12== | ==Problem 12== | ||
| + | Let <math>\triangle ABC</math> be a right triangle with right angle at <math>C.</math> Let <math>D</math> and <math>E</math> be points on <math>\overline{AB}</math> with <math>D</math> between <math>A</math> and <math>E</math> such that <math>\overline{CD}</math> and <math>\overline{CE}</math> trisect <math>\angle C.</math> If <math>\frac{DE}{BE} = \frac{8}{15},</math> then <math>\tan B</math> can be written as <math>\frac{m \sqrt{p}}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, and <math>p</math> is a positive integer not divisible by the square of any prime. Find <math>m+n+p.</math> | ||
== Solution == | == Solution == | ||
Revision as of 00:32, 17 March 2012
Problem 12
Let 
be a right triangle with right angle at 
Let 
and 
be points on 
with between 
and such that 
and 
trisect 
If 
then 
can be written as 
where 
and 
are relatively prime positive integers, and 
is a positive integer not divisible by the square of any prime. Find 
Solution
See also
| 2012 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
