Difference between revisions of "2005 AIME II Problems/Problem 15"

 
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== Solution ==
 
== Solution ==
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{{solution}}
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== See also ==
  
== See also ==
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*[[2005 AIME II Problems/Problem 14| Previous problem]]
 
* [[2005 AIME II Problems]]
 
* [[2005 AIME II Problems]]

Revision as of 21:15, 7 September 2006

Problem

Let $w_1$ and $w_2$ denote the circles $x^2+y^2+10x-24y-87=0$ and $x^2 +y^2-10x-24y+153=0,$ respectively. Let $m$ be the smallest possible value of $a$ for which the line $y=ax$ contains the center of a circle that is externally tangent to $w_2$ and internally tangent to $w_1.$ Given that $m^2=\frac pq,$ where $p$ and $q$ are relatively prime integers, find $p+q.$

Solution

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See also

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