How to delete unnecessary dot?

Edit (based on @chishimotoji's comment)

Only PointSymbolA=none is enough to delete the black bullet.

But, that is strange to me since the bullet is at point C in coordinates (0,8) (note the change of units).

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Pass the options PointSymbolA=none (and for other 2 points) to the \pstTriangle command.

\documentclass[border=15pt,pstricks,12pt]{standalone}
\usepackage{pst-eucl}

\begin{document}
\begin{pspicture}[showgrid](-5,-5)(10,10)
\psset{unit=2cm,PointSymbol=none,PointName=none}
\pstTriangle[%
  PointSymbolC=none,
  PointSymbolA=none,
  PointSymbolB=none
](0,4){C}(0,0){A}(3,0){B}
 %%% OR \pstTriangle[PointSymbol=none](0,4){C}(0,0){A}(3,0){B} 
\pstMiddleAB{A}{B}{I1} \pstArcOAB{I1}{A}{B}
\pstMiddleAB{B}{C}{I2} \pstArcOAB{I2}{B}{C}
\pstMiddleAB{C}{A}{I3} \pstArcOAB{I3}{C}{A}
\end{pspicture}
\end{document}

With version 1.63, available from http://archiv.dante.de/~herbert/TeXnik/tex/generic/pst-eucl/ or in the next two days with an update of the TeXLive or MikTeX:

\documentclass[border=15pt,pstricks,12pt]{standalone}
\usepackage{pst-eucl}

\begin{document}

\begin{pspicture}[showgrid](-2,-2)(2,2)
\pstGeonode[PointSymbol=none,PosAngle={0,90,180}](1.5,-1){A}(0,1){B}(-1,-.5){C}
\pspolygon[linejoin=2](A)(B)(C)
\pstTriangleIC[linecolor=red]{A}{B}{C}
\pstTriangleOC[linecolor=red]{A}{B}{C}
\end{pspicture}


\psset{unit=3cm}

\begin{pspicture}(2,2)
    \psset{PointSymbol=none,PointName=none}
    \pstGeonode(0,0){A}(1,0){B}(1,1){C}(0,1){D}
    \pswedge[fillstyle=solid,fillcolor=red](C){1}{135}{-45}
    \pstTranslation[PointSymbol=none]{D}{B}{C}[C1] 
    \pstTranslation[PointSymbol=none]{B}{D}{C}[C2]
    \pstInterLC[PointSymbol=none]{C1}{C2}{C}{B}{M1}{M2}
    \pstInterLC[PointSymbol=none]{A}{C1}{A}{M1}{M3}{M4}
    \pstInterLC[PointSymbol=none]{A}{C2}{A}{M2}{M5}{M6}
    \psarc(A){1.73205}{0}{90}
    \psline(M6)(A)(M4)
    \psdot*(C)
\end{pspicture}
\end{document}