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I want to draw two circles passing through the point M(-1, -4) and tangent to the lines 4x+ 3y = 0 and 3 x + 4 y + 1 = 0. The equation of circles are (x + 1)^2 + (y +2)^2 = 4 and (x +241)^2 + (y + 242)^2 = 338^2. The first circle has small radius and the second has big radius. It is difficult for me to view when I draw them. My code is (I draw with Geogebra).

\documentclass[12pt]{article}
\usepackage{pstricks-add}
\pagestyle{empty}
\begin{document}
\psset{xunit=0.5mm,yunit=0.5mm,algebraic=true,dimen=middle,dotstyle=o,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture}(-193.7,-54.03)(34.83,63.61)
\psplot[linewidth=1.2pt]{-193.7}{34.83}{(-0-4*x)/3}
\psplot{-193.7}{34.83}{(-1-3*x)/4}
\pscircle(-241,-242){338}
\pscircle(-1,-2){2}
\begin{scriptsize}
\psdots[dotstyle=*](-1,-4)
\rput[bl](-3.92,-6.74){$M$}
\end{scriptsize}
\end{pspicture}
\end{document}

enter image description here

enter image description here

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The best you can do, I think, is drawing the big circle alone first and, in a second figure, draw the small circle and a fraction of the big one, in the neighbourhood of the point M and tthe points of contact with their tangents. –  Bernard May 9 at 0:49

1 Answer 1

Here is a realisation of my suggestion: first, this:

\documentclass[12pt, pdf, x11names]{standalone}%

\usepackage{pstricks-add}
\usepackage{pst-eucl}
\usepackage{sansmath}

\begin{document}

\scriptsize\sffamily\sansmath
\noindent
\psset{unit=0.15mm}%
\begin{pspicture*}(-650,-650)(350,250)
\psaxes[ticks = all,ticksize = -2pt,   labels =all, Dx = 100,Dy = 100,](0,0)(-650,-650)(350,250)
\pscircle[linecolor = Gold2](-241,-242){338}
\pstGeonode[dotsize = 2pt](-1,-4){M}
\psset{PointName = none, PointSymbol = none,  nodesep = -600}
\pstGeonode(0,0){O}(3,-4){A}(-3,2){B}(5,-4){C}
\pstLineAB[linecolor = DeepSkyBlue2]{O}{A}\pstLineAB[linecolor = VioletRed3]{B}{C}
\pscircle[linecolor =DarkOliveGreen3](-1,-2){2}
\end{pspicture*}

\end{document} 

that gives this picture:

enter image description here

then almost the same code, that produces a ×100 zoom:

\documentclass[12pt, pdf, x11names]{standalone}%

\usepackage{pstricks-add}
\usepackage{pst-eucl}
\usepackage{sansmath}

\begin{document}

\scriptsize\sffamily\sansmath
\noindent
\psset{unit=1.5cm}
\begin{pspicture*}(-6.5,-6.5)(2.5,1.5)
\psaxes[ticks = all,ticksize = -2pt,   labels =all, linewidth = 0.6pt](0,0)(-6.5,-6.5)(3.5,2.5)
\pscircle[linecolor = Gold2](-241,-242){338}
\pstGeonode[dotsize = 2pt](-1,-4){M}
\psline[linewidth = 0.4pt, linestyle = dashed, dash = 2pt  3pt](0,-4)(M)(-1,0)
\psset{PointName = none, PointSymbol = none,  nodesep = -600}
\pstGeonode(0,0){O}(3,-4){A}(-3,2){B}(5,-4){C}
\pstLineAB[linecolor = DeepSkyBlue2]{O}{A}\pstLineAB[linecolor = VioletRed3]{B}{C}
\pscircle[linecolor =DarkOliveGreen3](-1,-2){2}
\end{pspicture*}

\end{document} 

and we get this:

enter image description here

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