\begin{pspicture}(-2,-4)(2,0.5)
  \pstTriangle[PosAngleB=-30]{A}(2.5;-90){B}(2.5;-60){C}
   \pstCircleOA{B}{C}
   {\psset{PosAngleA=30,PointSymbolB=none}
     \pstInterLC{A}{B}{B}{C}{M}{none}
     \pstInterLC{A}{C}{B}{C}{N}{none}}
   \psset{nodesep=-2}
   \pstLineAB{M}{N}
   \pstTranslation[PointSymbol=none]{N}{C}{M}{C2}
   \pstLineAB{C2}{C}
   \psset{arcsep=\pslinewidth,doubleline=true}
   \pstMarkAngle{N}{C}{C2}{}
   \pstMarkAngle[MarkAngleRadius=.3]{C2}{C}{B}{}
\end{pspicture}

\begin{pspicture}(-5.5,-2.5)(2.5,0.5)
\pstTriangle[PosAngleA=90,PosAngleB=100,PosAngleC=-80]
            {V}(-4,0){T}(2.1;-115){E}
\pstGeonode(2.1;0){U}
\pstTranslation{V}{E}{U}{N}
\pstSegmentMark{V}{E}\pstSegmentMark{E}{N}
\pstLineAB{V}{U}\pstLineAB{U}{N}
 
\pstTranslation[PosAngle=-90]{V}{T}{E}{R}
\pstLineAB{T}{R}\pstLineAB{R}{E}

\pstMiddleAB{V}{N}{S}
\end{pspicture}

\begin{pspicture}(-2.5,-1)(5,2.5)
\pstTriangle[PosAngleA=90,PosAngleB=-90,PosAngleC=-10](0,2){A}(-2,0){B}(4,0){C}
\pstProjection[PosAngle=-90]{B}{C}{A}{H}
\pstLineAB{A}{H}
\pstRightAngle{C}{H}{A}
\end{pspicture}

\begin{pspicture}(-1.5,-1.5)(6,1.5)
  \pstGeonode[PosAngle=180]{O}
  \pstGeonode(1;-30){A}
  %\pstGeonode(2;10){B}
  \pstCircleOA{O}{A}
  \pstCurvAbsNode{O}{A}{B}{\pstDistVal{1.5}}
  \ncline{O}{A}\ncline{O}{B}
  
  \pstTriangle[PosAngleA=-120,PosAngleC=100](4,0){I}(5,0){M}(4,1){N}
  \pstRightAngle{M}{I}{N}
  \pstCircleOA{I}{M}
\end{pspicture}

\begin{pspicture}(-2,-2)(2,2)
  \rput{10}{
  \pstGeonode[PosAngle=200](-1,-1){A}
  \pstGeonode[PosAngle=-20](1,-1){B}
  \pstGeonode[PosAngle=10](1,1){C}
  \pstGeonode[PosAngle=150](-1,1){D}
  \pspolygon(A)(B)(C)(D)
  \pstGeonode[PosAngle=90](0.75,1){M}
  \pstLineAB{M}{B}\pstLineAB{A}{M}
  \pstProjection[PosAngle=100,CodeFig=true,CodeFigColor=black]{A}{M}{B}{H}
}
\end{pspicture}

\begin{pspicture}(-.5,-1)(6.5,2.5)
\pstGeonode[PosAngle=-100]{A}
\pstGeonode(4,0){B}
\pstGeonode[PosAngle=90](6,2){C}
\pstGeonode[PosAngle=90](2,2){D}
\pspolygon(A)(B)(C)(D)
\psset{CodeFigColor=black}
\pstMiddleAB[CodeFig=true,PosAngle=120]{A}{D}{I}
\pstLineAB{I}{B}
\pstLineAB{A}{C}
\pstInterLL[PosAngle=90]{I}{B}{A}{C}{M}
\end{pspicture}

\begin{pspicture}(-.5,-.7)(6,3.5)
\pstTriangle[PosAngleA=-110,PosAngleC=90]{D}(4,0){C}(1.5,3){A}
\pstMiddleAB[PointSymbol=none]{A}{C}{I}
\pstSymO{I}{D}{B}
\pstLineAB{A}{B}\pstLineAB{B}{C}
\psset{CodeFig=true,CodeFigColor=black}
\pstProjection[PointSymbol=none]{A}{C}{B}{H1}
\pstProjection[PointSymbol=none]{B}{C}{A}{H2}
\psset{nodesep=-2}
\pstLineAB{A}{H2}
\pstLineAB{B}{H1}
\pstInterLL[PosAngle=90]{A}{H2}{B}{H1}{E}
\end{pspicture}

\begin{pspicture}(-2.5,-2.5)(2.5,2.5)%1.5)\psgrid
  \pstGeonode{O}
  \psset{nodesepB=-1}
  {\psset{PosAngle=-15}\pstGeonode(.7;20){A}  \pstGeonode(2;20){C}}
  {\psset{PosAngle=20}\pstGeonode(.7;80){B}  \pstGeonode(2;80){D}}
  \pstCircleOA{O}{A}
  \pstCircleOA{O}{C}
  \pstLineAB{O}{C}
  \pstLineAB{O}{D}
\end{pspicture}

\begin{pspicture}(-1,-1)(4,6)%5)\psgrid
  \pstTriangle[PosAngle=-55,PosAngleC=90]{A}(4;40){B}(6;60){C}
  \psset{CodeFig=true,CodeFigColor=black,nodesep=-1}
  \pstMiddleAB{A}{B}{I}
  \pstBissectBAC[PointSymbol=none]{C}{B}{A}{K1}
  {\psset{arcsep=\pslinewidth,doubleline=true}
    \pstMarkAngle{C}{B}{K1}{}
    \pstMarkAngle[MarkAngleRadius=.3]{K1}{B}{A}{}}

  \pstLineAB{K1}{B}
  \pstTranslation[PointSymbol=none]{B}{C}{I}{K2}
  \pstLineAB{K2}{I}
  \pstInterLL[PosAngle=35]{B}{K1}{I}{K2}{K}
%  \pstGeonode[PointName=(d)](0,4){d}
\end{pspicture}

\begin{pspicture}(-1,-1)(7,4)%3)\psgrid
  \pstGeonode[PosAngle=-90]{D}\pstGeonode(6;10){C}
  \pstGeonode(5;45){B}\pstGeonode[PosAngle=180](2;60){A}
  \pspolygon(A)(B)(C)(D)
  \pstMiddleAB[PosAngle=110]{A}{B}{I}
  \pstMiddleAB[PosAngle=-90]{C}{D}{K}
  \pstMiddleAB{B}{D}{P}
  \pstMiddleAB[PosAngle=90]{A}{C}{R}
  \pstMiddleAB[PosAngle=20]{I}{K}{Q}
  \ncline{A}{C}\ncline{D}{B}\ncline{I}{K}
\end{pspicture}

\begin{pspicture}(-1,-1)(5,3)
  \pstTriangle[PosAngleA=-90,PosAngleC=90]{A}(4;10){B}(2;100){C}
  \pstRightAngle{B}{A}{C}
  \pstProjection[CodeFig=true,CodeFigColor=black,PosAngle=30]{C}{B}{A}{H}
  \pstOrtSym{A}{B}{H}{K}
  \pstOrtSym{A}{C}{H}{L}
\end{pspicture}

\begin{pspicture}(-.5,-.5)(3.5,3.5)
  \pstGeonode[PosAngle=-110](0,0){A}
  \pstGeonode[PosAngle=-70](3,0){B}
  \pstGeonode[PosAngle=20](3,3){C}
  \pstGeonode[PosAngle=160](0,3){D}
  \psset{linewidth=1.5\pslinewidth}
  \pspolygon(A)(B)(C)(D)
  \pstMiddleAB[PosAngle=-90]{A}{B}{I}
  \pstMiddleAB{B}{C}{J}
  \pstMiddleAB[PosAngle=-90]{I}{B}{K}
  \pstProjection[PosAngle=170,CodeFig=true,CodeFigColor=black,
                 RightAngleSize=.2]{I}{C}{B}{H}
  \psline(I)(C)
  {\psset{linestyle=dashed}\psline(J)(H)\psline(H)(K)}
  \psset{arcsep=1.5\pslinewidth}
  {\psset{doubleline=true}
    \pstMarkAngle{H}{B}{K}{}
    \pstMarkAngle{K}{H}{B}{}}
  \pstMarkAngle{J}{B}{H}{}
  \pstMarkAngle[MarkAngleRadius=.5]{B}{H}{J}{}
\end{pspicture}

  \begin{pspicture}(-.5,-3)(6,5)
    \psset{unit=8mm}
    \pstTriangle[PosAngleA=180,PosAngleB=90](0,0){B}(6;60){A}(2.5;-30){C}
    \pstHomO[PosAngle=45,HomCoef=.8]{A}{C}{E}
    \pstCircleAB{A}{E}
    \pstMiddleAB[PointName=none]{A}{E}{O}
    \pstInterLC[PosAngleA=180,PointNameB=none]{B}{A}{O}{E}{F}{ff}
    \pstLineAB{E}{F}
    \pstRightAngle{E}{F}{A}
  \end{pspicture}

\begin{pspicture}(-3,-3)(3,3)
  \pstTriangle[PosAngleA=90,PosAngleB=180,PosAngleC=-10]
  (0,2){A}(-2,0){B}(2,-1){C}
  \pstCircleABC{A}{B}{C}{O}
  \psset{CodeFig=true, CodeFigColor=black, CodeFigStyle=solid}
  \pstProjection[PosAngle=130]{A}{B}{O}{I}
  \pstProjection{A}{C}{O}{J}
\end{pspicture}

\begin{pspicture}(-2,-1.5)(4,2.5)
  \newlength{\cc}
  \setlength{\cc}{2.2cm}
  \pstGeonode[PosAngle=200]{A}
  \pstGeonode[PosAngle=-70](\cc,0){B}
  \pstGeonode(\cc,\cc){C}
  \pstGeonode[PosAngle=180](0,\cc){D}
  \pstHomO[PosAngle=90,HomCoef=.3]{C}{D}{F}
  \pstHomO[PosAngle=180,HomCoef=-.3]{A}{D}{E}
  \pspolygon(A)(B)(C)(D) \psline(E)(F)
  \pstSegmentMark{F}{C} \pstSegmentMark{A}{E}
  \pcline(A)(0,-\cc)\aput(1){$y$}
\end{pspicture}