# [Tex/LaTex] Can PSTricks or others draw the 4 common tangent lines of 2 “disjoint” circles without having to do extra calculations

pstrickstikz-pgf

There are two disjoint circles. Their centers and radii are given.
Without doing extra calculations, can we draw the 4 tangent lines using PSTricks (preferred) or others?

I asked many Illustrator, Free-hand, CAD experts, they cannot do it exactly. ðŸ™‚

pstricks-add knows a macro for calculating and saving 10 points as nodes, the two central points and the four points on each circle. See the documentation (run texdoc pstricks-add) for the names:

\documentclass[pstricks,border=20pt]{standalone}

\begin{document}
\begin{pspicture}[showgrid](-2,-2)(10,10)
\pnodes(1,1){M1}(7,7){M2}
\pscircle(M1){1}\pscircle(M2){3}
\psCircleTangents(M1){1}(M2){3}
\pcline[nodesepA=-1cm,nodesepB=-4.5cm,linecolor=blue](CircleTO1)(CircleTO2)
\pcline[nodesepA=-1cm,nodesepB=-4.5cm,linecolor=blue](CircleTO3)(CircleTO4)
\pcline[nodesep=-1cm,linecolor=red](CircleTI1)(CircleTI2)
\pcline[nodesep=-1cm,linecolor=red](CircleTI3)(CircleTI4)
\psdots(M1)(M2)(CircleTC1)(CircleTC2)%
(CircleTO1)(CircleTO2)(CircleTO3)(CircleTO4)%
(CircleTI1)(CircleTI2)(CircleTI3)(CircleTI4)%
\end{pspicture}

\end{document}