Difference between revisions of "2013 AIME I Problems/Problem 13"
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== Problem 13 == | == Problem 13 == | ||
| − | + | Triangle <math>AB_0C_0</math> has side lengths <math>AB_0 = 12</math>, <math>B_0C_0 = 17</math>, and <math>C_0A = 25</math>. For each positive integer <math>n</math>, points <math>B_n</math> and <math>C_n</math> are located on <math>\overline{AB_{n-1}}</math> and <math>\overline{AC_{n-1}}</math>, respectively, creating three similar triangles <math>\triangle AB_nC_n \sim \triangle B_{n-1}C_nC_{n-1} \sim \triangle AB_{n-1}C_{n-1}</math>. The area of the union of all triangles <math>B_{n-1}C_nB_n</math> for <math>n\geq1</math> can be expressed as <math>\tfrac pq</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>q</math>. | |
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== Solution == | == Solution == | ||
Revision as of 13:28, 24 March 2013
Problem 13
Triangle 
has side lengths 
, 
, and 
. For each positive integer 
, points 
and 
are located on 
and 
, respectively, creating three similar triangles 
. The area of the union of all triangles 
for 
can be expressed as 
, where 
and 
are relatively prime positive integers. Find .
Solution
(solution)
See also
| 2013 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
