Difference between revisions of "2018 AMC 10A Problems/Problem 15"
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| − | Call the largest circle <math>\ | + | Call the largest circle <math>\circ X</math>. |
Revision as of 15:48, 8 February 2018
Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points 
and 
, as shown in the diagram. The distance 
can be written in the form 
, where 
and 
are relatively prime positive integers. What is 
?
![[asy] draw(circle((0,0),13)); draw(circle((5,-6.2),5)); draw(circle((-5,-6.2),5)); label("$B$", (9.5,-9.5), S); label("$A$", (-9.5,-9.5), S); [/asy]](http://latex.artofproblemsolving.com/c/1/d/c1d7b33c122356459463ccf321031d04f8f53752.png)
Solution
Call the largest circle 
.
