Difference between revisions of "2012 AIME I Problems/Problem 13"
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==Problem 13== | ==Problem 13== | ||
| + | Three concentric circles have radii <math>3,</math> <math>4,</math> and <math>5.</math> An equilateral triangle with one vertex on each circle has side length <math>s.</math> The largest possible area of the triangle can be written as <math>a + \frac{b}{c} \sqrt{d},</math> where <math>a,</math> <math>b,</math> <math>c,</math> and <math>d</math> are positive integers, <math>b</math> and <math>c</math> are relatively prime, and <math>d</math> is not divisible by the square of any prime. Find <math>a+b+c+d.</math> | ||
== Solution == | == Solution == | ||
Revision as of 00:34, 17 March 2012
Problem 13
Three concentric circles have radii 
and 
An equilateral triangle with one vertex on each circle has side length 
The largest possible area of the triangle can be written as 
where 
and 
are positive integers, 
and 
are relatively prime, and is not divisible by the square of any prime. Find 
Solution
See also
| 2012 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 | ||
