4

The circle Mixtilinear.

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath,amssymb,newcent}
\usepackage{pstricks} % required package
\usepackage{pst-node,pst-func,pst-plot,pst-eucl,pstricks-add,multido}
\usepackage{auto-pst-pdf} % required package
\begin{document}

\begin{pspicture}[showgrid](-3,-3)(8,8)
\pstTriangle(2,4){A}(0,0){B}(6,0){C}
\pstCircleABC[PosAngle=60]{A}{B}{C}{O}

{\psset{linestyle=none,PointName=none,PointSymbol=none}
\pstBissectBAC{B}{A}{C}{A'}
\pstBissectBAC{A}{C}{B}{C'}
 }
{\psset{PointName=none,PointSymbol=none}
\pstInterLL{A}{A'}{C}{C'}{E}
\pstMiddleAB{B}{C}{I}
\pstInterLC{O}{I}{O}{A}{D}{D'}
\pstInterLC{D}{E}{O}{A}{K}{F}
\pstInterLC{B}{E}{O}{A}{R}{Y}
 }
\pstInterLL[PosAngle=45]{F}{Y}{C}{A}{Z}
\pstSymO[PosAngle=135]{E}{Z}[Z']
\pstCircleABC[PosAngle=135]{F}{Z}{Z'}{X}
\end{pspicture}
\end{document}

The result of compiling:

enter image description here

How to show the point F?

Solution:

Add

\psdot(F)
\uput[-135](F){$F$}

Or

\pstInterLC[PointNameB=M,PosAngleB=-135,PointSymbolB=*]{D}{E}{O}{A}{K}{M}
  • 1
    Bad title as always. – Money Oriented Programmer Dec 9 '18 at 19:15
  • \pstInterLC[PosAngle=-80,PointName=default,PointSymbol=default]{D}{E}{O}{A}{K}{F} – Money Oriented Programmer Dec 9 '18 at 19:25
  • @ArtificialStupidity :-))))))))))))))))))))))))))))))))))) – Trong Vuong Dec 10 '18 at 0:49
  • 1
    \psdot[linecolor=red](F). will always work if you have no idea how to get the nodes marked by PointSymbol. – user2478 Dec 10 '18 at 7:03
4

Delete all points and/or lines which are not of interest ...

\documentclass[12pt,a4paper]{article}
\usepackage{pst-eucl}
\begin{document}

\psset{unit=0.75}
\begin{pspicture}[showgrid](-5,-5)(10,10)
\pstTriangle[fillstyle=solid,fillcolor=red!60,opacity=0.3](0,0){A}(6,0){B}(2,4){C}
\pstCircleABC[PosAngle=60]{A}{B}{C}{O}
\pstBissectBAC[linestyle=none]{B}{A}{C}{A'}
\pcline[linestyle=dotted,nodesepB=-5cm](A)(A')
\pcline[linestyle=dashed,nodesepB=-5cm](A)(B)
\pcline[linestyle=dashed,nodesepB=-5cm](A)(C)
\pstOutBissectBAC[PointSymbol=none,PointName=none,linestyle=none]{C}{B}{A}{CBA}
\pstOutBissectBAC[PointSymbol=none,PointName=none,linestyle=none]{A}{C}{B}{ACB}
\pstInterLL{B}{CBA}{C}{ACB}{M1}
\pstProjection[PointName=I_1]{A}{B}{M1}[Mab]
\pstCircleOA[linecolor=red!60]{M1}{Mab}
\pstCircleOA[linecolor=red!60,linestyle=dashed,Radius=\pstDistAB{M1}{Mab}]{A}{}
\pstInterCC[Radius=\pstDistAB{M1}{Mab}]{A}{}{M1}{}{P1}{P2}
\psdots(P1)(P2)
\pstBissectBAC[linestyle=none]{A}{B}{C}{B'}
\pstInterLL[PointName=none]{A}{A'}{B}{B'}{Mi}
\psRelNode[angle=90](Mi)(A'){1}{ABi}\psdot(ABi)
\pcline[linestyle=dotted,nodesepB=-3cm](ABi)(Mi)
\pstInterLL[PointName=none]{A}{B}{Mi}{ABi}{E}\psdot(E)
\pstProjection[PointName=none]{A}{B}{Mi}[D]\psdot(D)
\psRelNode[angle=90](E)(B){2}{E'}\psdot(E')
\pstInterLL[PointName=none]{A}{A'}{E}{E'}{X}\psdot(X)
\pstCircleOA[linecolor=blue,linewidth=1.5pt,
             fillstyle=solid,fillcolor=blue!50,opacity=0.3]{X}{E}
\pcline[linestyle=dotted](Mi)(D)
\pcline[linestyle=dotted](X)(E)
\end{pspicture}

\end{document}

enter image description here

and here the same with reduced points/circles:

\documentclass[12pt,a4paper]{article}
\usepackage{pst-eucl}
\begin{document}

\psset{unit=0.75}
\begin{pspicture}[showgrid](-1,-3)(7,5)
    \pstTriangle[fillstyle=solid,fillcolor=red!60,opacity=0.3](0,0){A}(6,0){B}(2,4){C}
    \pstCircleABC[PosAngle=60]{A}{B}{C}{O}
    \psset{PointSymbol=none,PointName=none,linestyle=none}
    \pstBissectBAC[linestyle=none]{B}{A}{C}{A'}
    \pstOutBissectBAC{C}{B}{A}{CBA}
    \pstOutBissectBAC{A}{C}{B}{ACB}
    \pstInterLL{B}{CBA}{C}{ACB}{M1}
    \pstProjection{A}{B}{M1}[Mab]
    \pstCircleOA[linecolor=red!60]{M1}{Mab}
    \pstBissectBAC[linestyle=none]{A}{B}{C}{B'}
    \pstInterLL[PointName=none]{A}{A'}{B}{B'}{Mi}
    \psRelNode[angle=90](Mi)(A'){1}{ABi}
    \pstInterLL[PointName=D,PointSymbol=*]{A}{B}{Mi}{ABi}{E}
    \pstProjection{A}{B}{Mi}[D]%\psdot(D)
    \psRelNode[angle=90](E)(B){2}{E'}%\psdot(E')
    \pstInterLL[PointName=m,PointSymbol=*]{A}{A'}{E}{E'}{X}
    \pstCircleOA[linecolor=blue,linewidth=1.5pt,linestyle=solid,
                fillstyle=solid,fillcolor=blue!50,opacity=0.3]{X}{E}
    \pstInterLC[PointSymbolA=none,PointSymbolB=*,PointNameB=F]{O}{X}{X}{E}{F1}{F2}
    \pstInterLC[PointSymbolA=none,PointSymbolB=*,PointNameB=E]{E}{ABi}{X}{E}{G1}{G2}
\end{pspicture}

\end{document}

enter image description here

2
\documentclass[12pt,pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}

\begin{document}
\begin{pspicture}[showgrid,PosAngle=30](-1,-3)(7,5)
\pstTriangle(2,4){A}(0,0){B}(6,0){C}
\pstCircleABC[PosAngle=60]{A}{B}{C}{O}
{
    \psset{linestyle=none,PointName=none,PointSymbol=none}  
    \pstBissectBAC{B}{A}{C}{A'}
    \pstBissectBAC{A}{C}{B}{C'}
}
{
    \psset{PointName=none,PointSymbol=none}
    \pstInterLL{A}{A'}{C}{C'}{E}
    \pstMiddleAB{B}{C}{I}
    \pstInterLC[PosAngle=-80]{O}{I}{O}{A}{D}{D'}
    \pstInterLC[PosAngle=-80,PointName=default,PointSymbol=default]{D}{E}{O}{A}{K}{F}
    \pstInterLC[PosAngle=-80]{B}{E}{O}{A}{R}{Y}
}
\pstInterLL[PosAngle=45]{F}{Y}{C}{A}{Z}
\pstSymO[PosAngle={150}]{E}{Z}[Z']
\pstCircleABC[PosAngle=-90]{F}{Z}{Z'}{X}
\end{pspicture}
\end{document}

enter image description here

  • :-))))))))))))))))) – Trong Vuong Dec 10 '18 at 8:24

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