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I am trying to calculate the touching point of two circles. I have the following information.

Circle $1$:

  • Centre $(h,k)$
  • Radius $r_1$

Circle $2$:

  • Point on Circumference $(x_1,y_1)$
  • Radius $r_2$

From this I would like to calculate the centre point of circle $2$: $(s,r)$ and the point where they touch: $(x,y)$.

I have worked out that to find the second centre point I can express the formulas like this:

$$(x_1-s)^2+(y_1-r)^2=r_2^2$$

$$(s-h)^2+(r-k)^2=(r_1+r_2)^2$$

Unforunately my maths skills are not up to the task of solving these equations for $s$ and $r$, and ultimately for $x$ and $y$.

I would appreciate any help that can be provided.

Regards

Martin.

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    Are the circles supposed to be tangent, so there is only one point where they touch? If not, I don't think there is enough information. Even so, I believe there are two solutions.2011-02-21
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    Yes They are tangential. I am looking to find that point of tangentiality. I think there can only be one solution if it is tangential. - Martin.2011-02-21
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    @Isaac. Thank you for help. You've given me the answer I needed. Regards Martin.2011-02-23
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    @Martin: please do not use answers to make comments. You should be able to comment on answers to your own questions even at low reputation.2011-02-23

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