Difference between revisions of "AoPS Wiki:Problem of the Day/August 25, 2011"
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− | + | 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>. |
Latest revision as of 23:29, 24 August 2011
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
.