I'm trying to find the lines tangent to two circles. I've seen several examples but with poorlyy explained methods. Given the circle


and the the line equation


one of the method is based on the relation


Can you tell me what relation is this? How it was obtained? Thank you.


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    $\begingroup$ I'm voting to close this question as off-topic because of no mathematica related content $\endgroup$ – george Jun 12 '16 at 23:46
  • $\begingroup$ As posed this seems more a question about the math than about Mathematica, so it may not be appropriate for this forum. Even then, you may want to clarify your question: what is the exact relationship between the line and the two circles? As posed, there are infinite lines that are tangent to two arbitrary circles, so the problem seems underdetermined. $\endgroup$ – MarcoB Jun 12 '16 at 23:47
  • $\begingroup$ Let $C: (x-x_{0})^2+(y-y_{0})^2=r_{1}^2$ and $L: y=ax+b$. Putting L into C, we get a new quadratic equation in x. Since L is tangent to C, the discriminant of it should be equal to 0. I think, after simplification, we should get the mentioned expression, which is then the condition for tangency. $\endgroup$ – Mick Jun 13 '16 at 4:10

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