[Tex/LaTex] How to draw a tangent ending smoothly in a circle

tikz-pgf

I'm trying to draw a tanget on a circle, but I'm not happy with the result I get from the tangent option.

all
particularly, I'd like to have the lines ending smoothly in the circle. The problem is shown enlarged here:

enlarge1
enlarge2

Here is the code for this mininmal example

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
  \begin{tikzpicture}[thick]
    \node[draw,circle,xshift=2.2cm] (big) [minimum size=25mm] {};
    \node[draw,circle] (small) [minimum size=2mm] {};
    \draw (small.south) -- (tangent cs:node=big,point={(small.south)});
    \draw (small.north) -- (tangent cs:node=big,point={(small.north)},solution=2);
   \end{tikzpicture}
\end{document}

I'd greatly appreciate any advice allowing me to do this!

Best Answer

You already have the solution: Just apply the same to the small circle, and throw some outer sep=0 for a nice blend. 

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

  \begin{tikzpicture}[thick]
    \node[draw,circle,xshift=2.2cm,minimum size=25mm,outer sep=0] (big) {};
    \node[draw,circle,minimum size=2mm,outer sep=0] (small) {};
    \draw (tangent cs:node=small,point={(big.south)},solution=2) -- (tangent cs:node=big,point={(small.south)});
    \draw (tangent cs:node=small,point={(big.north)},solution=1) -- (tangent cs:node=big,point={(small.north)},solution=2);
   \end{tikzpicture}

\end{document}

enter image description here

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