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),</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> iare 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 07:06, 8 October 2007
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
iare 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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