CONST 
  LightColor = Color.Grey50, 
  LightWidth = 1.5, 
  SoftRed = Color.FromHSV(Color.RedHue, 0.5, 1), 
  SoftBlue = Color.FromHSV(Color.BlueHue, 0.5, 1), 
  SoftGreen = Color.FromHSV(Color.GreenHue, 0.8, 0.5), 
  SoftMagenta = Color.FromHSV(Color.MagentaHue, 0.5, 1);

PROC Label(name) IS 
  SAVE PS IN 
    PS.SetFont("Helvetica", PS.Huge); 
    TypeLinesC.Center((0, 200), name) 
  END 
END;

UI TextTool(Label);

FUNC d = PerpPoint(a, b, c) IS 
  (E x = (100, 0) REL (a, b) :: 
    Angle.Right(x, d, c) AND Geometry.Colinear(a, d, x)) 
END;

UI PointTool(PerpPoint);

PROC DrawLine(a, b) IS 
  SAVE PS IN 
    PS.SetWidth(LightWidth); 
    PS.MoveTo(a); 
    PS.LineTo(b); 
    PS.Stroke() 
  END 
END;

UI PointTool(DrawLine);

PROC DrawPerp(a, b, c) IS 
  IF 
    VAR d ~ (0.1, 0) REL (b, c), f ~ (0.1, 0) REL (b, a) IN 
      Geometry.Colinear(a, f, b) AND 
      Geometry.Colinear(b, d, c) AND 
      (f, b) CONG (b, d) AND 
      Geometry.Dist(f, b) = 10 -> 
        IF 
          VAR e ~ (0.5, 0.2) REL (f, b) IN 
            (f, e) PARA (b, c) AND (a, b) PARA (e, d) -> 
              SAVE PS IN 
                PS.SetWidth(LightWidth); 
                PS.MoveTo(c); 
                PS.LineTo(b); 
                PS.MoveTo(d); 
                PS.LineTo(e); 
                PS.LineTo(f); 
                PS.MoveTo(a); 
                PS.LineTo(b); 
                PS.Stroke() 
              END 
          END 
        FI 
    END 
  FI 
END;

UI PointTool(DrawPerp);

PROC Connect3(a, b, c) IS 
  SAVE PS IN 
    PS.MoveTo(a); 
    PS.LineTo(c); 
    PS.LineTo(b); 
    PS.SetWidth(LightWidth); 
    PS.Stroke() 
  END 
END;

UI PointTool(Connect3);

PROC Start() IS 
  VAR 
    a = (-164.4, -182.8), b = (187.8, -78.12), 
    c = (19.69, 149.4) 
  IN 
    SAVE PS IN 
      Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
    END 
  END 
END;

UI Template(Start);

PROC Orthocenter() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), g ~ (95.47, -105.6), 
      h ~ (113.5, 22.5), i ~ (-37.27, 46.61), 
      j ~ (67.5, -11.45) 
    IN 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) -> 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j) 
        END; 
        Label("Orthocenter") 
    END 
  FI 
END;

UI Template(Orthocenter);

PROC Centroid() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      m ~ (14.36, -37.17) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      Geometry.Colinear(a, m, e) AND 
      Geometry.Colinear(b, m, f) -> 
        SAVE PS IN 
          PS.SetColor(SoftMagenta); 
          DrawLine(c, d); 
          DrawLine(b, f); 
          DrawLine(a, e) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(Color.Magenta); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(m) 
        END; 
        Label("Centroid") 
    END 
  FI 
END;

UI Template(Centroid);

PROC Circumcenter() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      k ~ (-12.2, -50.03) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) -> 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k) 
        END; 
        Label("Circumcenter") 
    END 
  FI 
END;

UI Template(Circumcenter);

PROC AllThree() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      g ~ (95.47, -105.6), h ~ (113.5, 22.5), 
      i ~ (-37.27, 46.61), j ~ (67.5, -11.45), 
      k ~ (-12.2, -50.03), m ~ (14.36, -37.17) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) AND 
      Geometry.Colinear(a, m, e) AND 
      Geometry.Colinear(b, m, f) -> 
        SAVE PS IN 
          PS.SetColor(SoftMagenta); 
          DrawLine(c, d); 
          DrawLine(b, f); 
          DrawLine(a, e) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j); 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k); 
          PS.SetColor(Color.Magenta); 
          PtLabel.None(m) 
        END 
    END 
  FI 
END;

UI Template(AllThree);

PROC EulerLine() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      g ~ (95.47, -105.6), h ~ (113.5, 22.5), 
      i ~ (-37.27, 46.61), j ~ (67.5, -11.45), 
      k ~ (-12.2, -50.03), m ~ (14.36, -37.17) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) AND 
      Geometry.Colinear(a, m, e) AND 
      Geometry.Colinear(b, m, f) -> 
        SAVE PS IN 
          PS.SetColor(SoftMagenta); 
          DrawLine(c, d); 
          DrawLine(b, f); 
          DrawLine(a, e) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        SAVE PS IN 
          PS.MoveTo(j); 
          PS.LineTo(k); 
          PS.SetWidth(1.5 * LightWidth); 
          PS.SetColor(Color.Black); 
          PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j); 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k); 
          PS.SetColor(Color.Magenta); 
          PtLabel.None(m) 
        END 
    END 
  FI 
END;

UI Template(EulerLine);

PROC EulerMidpoint() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      g ~ (95.47, -105.6), h ~ (113.5, 22.5), 
      i ~ (-37.27, 46.61), j ~ (67.5, -11.45), 
      k ~ (-12.2, -50.03), l ~ (27.65, -30.74) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) AND 
      l = Geometry.Mid(j, k) -> 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        SAVE PS IN 
          PS.MoveTo(j); 
          PS.LineTo(k); 
          PS.SetWidth(1.5 * LightWidth); 
          PS.SetColor(Color.Black); 
          PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(SoftGreen); 
          PtLabel.None(l); 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j); 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k) 
        END 
    END 
  FI 
END;

UI Template(EulerMidpoint);

PROC Feuerbach() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      g ~ (95.47, -105.6), h ~ (113.5, 22.5), 
      i ~ (-37.27, 46.61), j ~ (67.5, -11.45), 
      k ~ (-12.2, -50.03), l ~ (27.65, -30.74) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) AND 
      l = Geometry.Mid(j, k) -> 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        SAVE PS IN 
          PS.MoveTo(j); 
          PS.LineTo(k); 
          PS.SetWidth(1.5 * LightWidth); 
          PS.SetColor(Color.Black); 
          PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(SoftGreen); 
          PtLabel.None(l); 
          Circle.Draw(l, e); 
          PS.Stroke(); 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j); 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k) 
        END 
    END 
  FI 
END;

UI Template(Feuerbach);

PROC NinePoint() IS 
  IF 
    VAR 
      a = (-164.4, -182.8), b = (187.8, -78.12), 
      c = (19.69, 149.4), d ~ (11.7, -130.5), 
      e ~ (103.7, 35.64), f ~ (-72.35, -16.7), 
      g ~ (95.47, -105.6), h ~ (113.5, 22.5), 
      i ~ (-37.27, 46.61), j ~ (67.5, -11.45), 
      k ~ (-12.2, -50.03), l ~ (27.65, -30.74), 
      m ~ (-48.45, -97.13), n ~ (127.6, -44.79), 
      o ~ (43.59, 68.97) 
    IN 
      d = Geometry.Mid(a, b) AND 
      e = Geometry.Mid(b, c) AND 
      f = Geometry.Mid(a, c) AND 
      g = PerpPoint(a, b, c) AND 
      h = PerpPoint(b, c, a) AND 
      i = PerpPoint(c, a, b) AND 
      Geometry.Colinear(c, j, g) AND 
      Geometry.Colinear(i, j, b) AND 
      Angle.Right(a, d, k) AND 
      Angle.Right(c, f, k) AND 
      l = Geometry.Mid(j, k) AND 
      m = Geometry.Mid(a, j) AND 
      n = Geometry.Mid(b, j) AND 
      o = Geometry.Mid(c, j) -> 
        SAVE PS IN 
          PS.SetColor(SoftRed); 
          DrawPerp(a, g, c); 
          DrawPerp(b, h, a); 
          DrawPerp(c, i, b); 
          Connect3(b, i, j); 
          Connect3(c, g, j); 
          Connect3(a, h, j) 
        END; 
        SAVE PS IN 
          PS.SetColor(SoftBlue); 
          DrawPerp(a, d, k); 
          DrawPerp(c, f, k); 
          DrawPerp(b, e, k) 
        END; 
        SAVE PS IN 
          Triangle.Draw(a, b, c); PS.SetWidth(2); PS.Stroke() 
        END; 
        SAVE PS IN 
          PS.MoveTo(j); 
          PS.LineTo(k); 
          PS.SetWidth(1.5 * LightWidth); 
          PS.SetColor(Color.Black); 
          PS.Stroke() 
        END; 
        PtLabel.SetDotSize(4); 
        SAVE PS IN 
          PS.SetColor(SoftGreen); 
          PtLabel.None(l); 
          PtLabel.None(m); 
          PtLabel.None(n); 
          PtLabel.None(o); 
          Circle.Draw(l, e); 
          PS.Stroke(); 
          PS.SetColor(Color.Red); 
          PtLabel.None(i); 
          PtLabel.None(h); 
          PtLabel.None(g); 
          PtLabel.None(j); 
          PS.SetColor(Color.Blue); 
          PtLabel.None(d); 
          PtLabel.None(e); 
          PtLabel.None(f); 
          PtLabel.None(k) 
        END 
    END 
  FI 
END;

UI Template(NinePoint);