What is the syntax for creating "trace" in PSTricks?

For a static locus, it's easy doing first some geometry: it is a circle passing through the points I and J, which are 1/3 of AD, from A and D respectively. The points I and J themselves are not part of the locus. So it is enough to determine a third point, say the center of gravity K of triangle EAD, where E is equidistant from A and D, on the circle, and to draw the circumcircle of triangle KAD.

Here is a code

\documentclass[border=10pt, svgnames, pstricks]{standalone}

\usepackage{pst-eucl, auto-pst-pdf}

\begin{document}

\begin{pspicture}[showgrid](-4,-4)(4,4)
\pstGeonode[PosAngle={-45,-135,45,120,-75,45}](3;-47){A}(3;-130){D}(3;15){C}(3;120){C_1}(3;-75){C_2}(0,0){O}
\pnode(3;88.5){E}
\pstCircleOA{O}{A}
\pspolygon(A)(C)(D)
\pstCGravABC[PosAngle=60, PointSymbol=none, PointName={}]{A}{D}{E}{K}
\pstCGravABC[PosAngle=60]{A}{D}{C}{G}
\midAB(A)(D){H}
\pstHomO[HomCoef=0.3333, PointNameSep=0.8em, PosAngle ={-70,-110},PointSymbol=none]{H}{A,D}[I, J]
\pstTriangleOC[linecolor=IndianRed, linewidth=1.5pt]{I}{J}{K}
\psdots[dotstyle=o](I)(J)
\pstCGravABC[PosAngle=120]{A}{D}{C_1}{G_1}
\pstCGravABC[PosAngle=-75, PointNameSep=0.8em]{A}{D}{C_2}{G_2}
\end{pspicture}

\end{document}

\documentclass[border=10pt,pstricks]{standalone}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}[showgrid](-4,-4)(4,4)
\pstGeonode[PosAngle={-45,-135}](3;-47){A}(3;-130){D}(0,0){O}
\pstCircleOA{O}{A}
\pstGeonode[PosAngle=45](3;-40){C}
\pspolygon[linewidth=0.1pt,linestyle=dotted](A)(C)(D)
\pstCGravABC[PosAngle=60]{A}{D}{C}{G0}
\multido{\iA=-40+10}{35}{%
  \pstGeonode[PointName=none](3;\iA){C}
  \pspolygon[linewidth=0.1pt,linestyle=dotted](A)(C)(D)
  \pstCGravABC[PointName=none]{A}{D}{C}{G}
  \psline[linecolor=red,linewidth=2pt](G0)(G)
  \pnode(G){G0}
}
\end{pspicture}
\end{document}

\documentclass[border=10pt,pstricks]{standalone}
\usepackage{pst-eucl,multido,xfp}
\begin{document}

\def\step{10}

\multido{\iG=0+1,\iA=0+\step,\iD=-47+\step,\iE=145+\step}{\inteval{360/\step+1}}{%
  \begin{pspicture}[showgrid](-4,-4)(4,4)
    \pstGeonode[PointSymbol=none,PointName=none](3;0){a}(3;-47){c}(3;145){d}
    \pstTriangle(3;\iD){A}(3;\iA){C}(3;\iE){D}
    \pstCircleOA{0,0}{A}
    \pstCGravABC{a}{c}{d}{G0}
      \multido{\ix=0+1,\iy=1+1,\ia=\step+\step,\id=\inteval{-47+\step}+\step,\ie=\inteval{145+\step}+\step}{\iG}{%
        \pstGeonode[PointSymbol=none,PointName=none](3;\id){a}(3;\ia){c}(3;\ie){d}
        \pstCGravABC[PointSymbol=none,PointName=none]{a}{d}{c}{G\iy}
        \psline[linecolor=red,linewidth=2pt](G\ix)(G\iy)
      }%
  \end{pspicture}}%
\end{document}