Gold Arbelos

[PDF] [TEX]

 

 \documentclass[margin = 12 pt]{standalone}
 \usepackage{tkz-euclide}
 \usepackage{tkz-elements}

 \tikzset{new/.style={color=orange,ultra thin}} 
 \tikzset{step 1/.style={color=cyan,ultra thin}} 
 \tikzset{step 2/.style={color=purple,ultra thin}} 
 \begin{document}
 \begin{elements}
 scale =1 
 
 z.A      = point : new (0,0)
 z.B      = point : new (10,0)
 z.C      = gold_segment_ (z.A,z.B)

 z.O_1    = midpoint_ (z.A,z.B)
 z.O_2    = midpoint_ (z.A,z.C)
 z.O_3    = midpoint_ (z.C,z.B)

 z.Q      = north_pole_ (z.A,z.B)
 z.P      = north_pole_ (z.C,z.B)

 z.M_0    = div_harmonic_ext_ (z.O_2,z.O_3,z.C)
 z.M_1    = div_harmonic_int_ (z.O_1,z.O_2,z.A)
 z.M_2    = div_harmonic_int_ (z.O_1,z.O_3,z.B)

 z.S      = intersection_ll_ (z.B,z.Q,z.A,z.P)
 _,z.P_1  = intersection_lc_ (z.C,z.S,z.O_1,z.A)
  z.P_3   = intersection_cc_ (z.M_1,z.A,z.O_3,z.B)
  z.P_2   = intersection_cc_ (z.M_2,z.B,z.O_3,z.B)
 
  z.O_4   = circum_center_    (z.P_1,z.P_2,z.P_3)
  z.O_5   = circum_center_    (z.C,z.P_2,z.P_3)
 
 _,z.O_6  = intersection_lc_ (z.C,z.O_5,z.O_5,z.C)
 z.x      = rotation_         (z.C,math.pi/2,z.B)
  z.D,_   = intersection_lc_ (z.C,z.x,z.O_1,z.A)
 z.O_7    = midpoint_ (z.C,z.D)
 z.U,z.V  = intersection_cc_ (z.D,z.C,z.O_1,z.B)
 z.R      = projection_(z.U,z.V,z.O_2)
 z.S      = projection_(z.U,z.V,z.O_3)
 z.W      = intersection_ll_ (z.U,z.V,z.O_1,z.D)
 z.O      = inversion_ (z.D,z.C,z.W)
 \end{elements}
 
  \begin{tikzpicture}
    \tkzGetNodes(z)

    \tkzDrawCircles[teal](O_1,B)
    \tkzDrawSemiCircles[thin,teal](O_2,C O_3,B)
    \tkzDrawArc[purple,delta=0](D,V)(U)
    \tkzDrawCircle[new](O_7,C)
    \tkzDrawSegments[thin,purple](A,D D,B C,R C,S C,D U,V)
    \tkzDrawSegments[thin,red](O,D A,O O,B)
    \tkzDrawPoints(A,B,C,D,O_7)
    \tkzDrawPoints(O_1,O_2,O_3,U,V,R,S,W,O)
    \tkzDrawSegments[cyan](O_3,S O_2,R)
    \tkzDrawSegments[very thin](A,B)
    \tkzDrawSegments[cyan,thin](C,U U,D)
    \tkzMarkRightAngles[size=.2,fill=gray!40,opacity=.4](D,C,A A,D,B
      D,S,C D,W,V O_3,S,U O_2,R,U)
    \tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_1
      C,D,B D,C,R B,C,S A,R,O_2)
    \tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D
      D,B,C R,C,A O_3,S,B)
    \tkzLabelPoints[below](C,O_2,O_3,O_1)
    \tkzLabelPoints[above](D)
    \tkzLabelPoints[below](O)
    \tkzLabelPoints[below left](A)
    \tkzLabelPoints[above left](R)
    \tkzLabelPoints[above right](S)
    \tkzLabelPoints[left](V)
    \tkzLabelPoints[below right](B,U,W,O_7)
  \end{tikzpicture}
 

 \end{document}