Ryfujk

I have the following code:

begin {tikzpicture}[-latex ,auto ,node distance =0.8cm and 0.8cm ,on grid,

thin , state/.style ={ circle ,top color = black, bottom color = black,

draw,black , text=black, minimum width =0.01 cm}]

node[state] (a1) {};

node[state] (b1) [below =of a1]{};

node[state] (c1) [right =of a1]{};

node[state] (d1) [below =of c1]{};

node[shape=circle, draw=black, minimum size = 4cm, fit={(a1)(d1)}]{};

node[state] (a2) [right=7cm of a1] {};

node[state] (b2) [right =of a2] {};

node[state] (c2) [below =of a2] {};

node[state] (d2) [right =of c2] {};

node[state] (d3) [above =3cm of d2] {};

node[state] (d4) [right =2cm of d2] {};

node[state] (d5) [below =2cm of d2] {};

node[state] (d6) [above = of d4] {};

node[state] (d6) [above = of d6] {};

node[shape=circle,

      draw=black,

      minimum size=3cm,

      fit={(a2)(d2)}]{};

node[shape=circle, draw=black, fit={(d2)(d3)(d4)(d5)}]{};

path (b1) edge [bend right=0] node[] {} (a2);

end{tikzpicture} newline newline

This produces:

I'd like to draw a lines as shown below:

This is a possible solution, but I don't think it is the best way.

Add names for the circles.

documentclass[tikz,margin=3mm]{standalone}

usetikzlibrary{positioning,fit}

begin{document}

begin {tikzpicture}[,auto ,node distance =0.8cm and 0.8cm ,on grid,

thin , state/.style ={ circle ,top color = black, bottom color = black,

draw,black , text=black, minimum width =0.01 cm}]

node[state] (a1) {};

node[state] (b1) [below =of a1]{};

node[state] (c1) [right =of a1]{};

node[state] (d1) [below =of c1]{};

node[shape=circle, draw=black, minimum size = 4cm, fit={(a1)(d1)}] (circle1) {};

node[state] (a2) [right=7cm of a1] {};

node[state] (b2) [right =of a2] {};

node[state] (c2) [below =of a2] {};

node[state] (d2) [right =of c2] {};

node[state] (d3) [above =3cm of d2] {};

node[state] (d4) [right =2cm of d2] {};

node[state] (d5) [below =2cm of d2] {};

node[state] (d6) [above = of d4] {};

node[state] (d6) [above = of d6] {};

node[shape=circle,

      draw=black,

      minimum size=3cm,

      fit={(a2)(d2)}] (circle2) {};

node[shape=circle, draw=black, fit={(d2)(d3)(d4)(d5)}]{};

path[-latex] (b1) edge [bend right=0] node[] {} (a2);

draw[thick,red] (circle1.north)--(circle2.north);

draw[thick,red] (circle1.south)--(circle2.south);

end{tikzpicture}

end{document} 

AFAIK the first way to draw a tangent at two circles has been proposed in this nice answer. However, can't refrain from using this one.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{calc,positioning,fit}

begin{document}

begin{tikzpicture}[tangent of circles/.style args={%

at #1 and #2 with radii #3 and #4}{insert path={%

let p1=($(#2)-(#1)$),n1={atan2(y1,x1)},n2={veclen(y1,x1)*1pt/1cm},

    n3={atan2(#4-#3,n2)}

     in ($(#1)+(n3+n1+90:#3)$) -- ($(#2)+(n3+n1+90:#4)$)}},-latex ,auto ,node distance =0.8cm and 0.8cm ,on grid,

thin , state/.style ={ circle ,top color = black, bottom color = black,

draw,black , text=black, minimum width =0.01 cm}]

  node[state] (a1) {};

  node[state] (b1) [below =of a1]{};

  node[state] (c1) [right =of a1]{};

  node[state] (d1) [below =of c1]{};

  node[shape=circle, draw=black, minimum size = 4cm, fit={(a1)(d1)}]

  (circ1){};

  node[state] (a2) [right=7cm of a1] {};

  node[state] (b2) [right =of a2] {};

  node[state] (c2) [below =of a2] {};

  node[state] (d2) [right =of c2] {};

  node[state] (d3) [above =3cm of d2] {};

  node[state] (d4) [right =2cm of d2] {};

  node[state] (d5) [below =2cm of d2] {};

  node[state] (d6) [above = of d4] {};

  node[state] (d6) [above = of d6] {};

  node[shape=circle,

        draw=black,

        minimum size=3cm,

        fit={(a2)(d2)}] (circ2){};

  node[shape=circle, draw=black, fit={(d2)(d3)(d4)(d5)}]{};

  path (b1) edge [bend right=0] node[] {} (a2);

  draw[red,-,tangent of circles={at circ1.center and circ2.center with radii 2

  and 1.5}];

  draw[red,-,tangent of circles={at circ2.center and circ1.center with radii

  1.5 and 2}];

end{tikzpicture} 

end{document}