PSTricks: Perpendicular bisectors of line segments using pst-eucl

Question

First: This is a crosspost from the LaTeX Community since I haven't gotten any answer there.

Consider the following MWE:

\documentclass{article}

\usepackage{pst-eucl}

\begin{document}

\begin{figure}
 \centering
  \begin{pspicture}(10.5,9.8)
   \pnode(0,2.3){A}
   \pnode(3.7,7.8){B}
   \pnode(10.5,9.8){C}
   \psdot(A)
   \psdot(B)
   \psdot(C)
   \psline(A)(B)(C)
  \psset{
   PointSymbol=none,
   PointNameB=none,
   CodeFig=true,
   CodeFigColor=black
  }
   \pstMediatorAB{B}{A}{M}{M''}
   \pstMediatorAB{C}{B}{M'}{M'''}
  \end{pspicture}
\end{figure}

\end{document}

Is it possible to

(1) remove M and M' from the figure and

(2) extend the lines in order to make them intersect?

Ad (1): I tried to make the third argument blank but that is not legal.

Thank you in advance!

P.S. I know that it can be achieved with the following but I would like to do it with pst-eucl only:

\documentclass{article}

\usepackage{pst-eucl,pstricks-add}

\begin{document}

\begin{figure}
 \centering
  \begin{pspicture}(10.5,9.8)
   \pnode(0,2.3){A}
   \pnode(3.7,7.8){B}
   \pnode(10.5,9.8){C}
   \psdot(A)
   \psdot(B)
   \psdot(C)
   \psline(A)(B)(C)
  \psset{
   PointSymbol=none,
   PointNameB=none,
   CodeFig=true,
   CodeFigColor=black
  }
   \psRelLine(A)(B){1 2 div}{I'}
   \psRelLine[angle=90](I')(A){3}{I''}
   \psRelLine(B)(C){1 2 div}{J'}
   \psRelLine[angle=90](J')(B){2.8}{J''}
   \psIntersectionPoint(I')(I'')(J')(J''){X}
   \pcline(I')(X)
   \pcline(J')(X)
   \pstRightAngle{A}{I'}{I''}
   \pstRightAngle{B}{J'}{J''}
  \end{pspicture}
\end{figure}

\end{document}

Answer 1

\documentclass{article}
\usepackage{pst-eucl}    
\begin{document}

\begin{pspicture}(10.5,9.8)
  \pstGeonode[PointName=none](0,2.3){A}(3.7,7.8){B}(10.5,9.8){C}
  \psline(A)(B)(C)
\psset{
   PointSymbol=none,
   PointName=none,
   CodeFig=true,
   CodeFigColor=black}
   \pstMediatorAB[nodesepB=-6.5cm]{B}{A}{M}{M''}
   \pstMediatorAB[nodesepB=-6.5cm]{C}{B}{M'}{M'''}
\end{pspicture}

\end{document}