Difference between revisions of "2002 AIME II Problems/Problem 15"
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== Problem == | == Problem == | ||
| − | Circles <math>\mathcal{C}_{1}</math> and <math>\mathcal{C}_{2}</math> intersect at two points, one of which is <math>(9,6) | + | Circles <math>\mathcal{C}_{1}</math> and <math>\mathcal{C}_{2}</math> intersect at two points, one of which is <math>(9,6)</math>, and the product of the radii is <math>68</math>. The x-axis and the line <math>y = mx</math>, where <math>m > 0</math>, are tangent to both circles. It is given that <math>m</math> can be written in the form <math>a\sqrt {b}/c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers, <math>b</math> is not divisible by the square of any prime, and <math>a</math> and <math>c</math> are relatively prime. Find <math>a + b + c</math>. |
== Solution == | == Solution == | ||
Revision as of 12:42, 19 April 2008
Problem
Circles 
and 
intersect at two points, one of which is 
, and the product of the radii is 
. The x-axis and the line 
, where 
, are tangent to both circles. It is given that 
can be written in the form 
, where 
, 
, and 
are positive integers, is not divisible by the square of any prime, and and are relatively prime. Find 
.
Solution
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See also
| 2002 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
