;Task:
Implement a solution to the Problem of Apollonius &nbsp; ([[wp:Problem_of_Apollonius|description on Wikipedia]]) &nbsp; which is the problem of finding the circle that is tangent to three specified circles &nbsp; (colored black in the diagram below to the right). 

There is an &nbsp; [[wp:Problem_of_Apollonius#Algebraic_solutions|algebraic solution]] &nbsp; which is pretty straightforward. 


The solutions to the example in the code are shown in the diagram &nbsp; (below and to the right). 

The red circle is "internally tangent" to all three black circles, &nbsp; and the green circle is "externally tangent" to all three black circles.
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