Gold Arbelos

[PDF] [TEX]

 
% !TEX TS-program = lualatex
% Author Alain Matthes 2023
\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{tkzelements} 
z.A      = point:    new (0,0)
z.B      = point:     new (10,0)
L.AB     = line:     new ( z.A, z.B )
z.C      = L.AB:     gold_ratio ()
L.AC     = line:     new ( z.A, z.C )
L.CB     = line:     new ( z.C, z.B )
z.O_0    = L.AB.mid
z.O_1    = L.AC.mid
z.O_2    = L.CB.mid
C.AB     = circle:   new ( z.O_0, z.B ) 
C.AC     = circle:   new ( z.O_1, z.C ) 
z.D,_    = intersection ( C.AC: tangent_at (z.C), C.AB )
L.CD     = line: new ( z.C,z.D )
z.O_7    = L.CD.mid
C.DC     = circle:   new ( z.D,z.C )
z.V,z.U  = intersection (C.DC,C.AB)
L.UV     = line: new ( z.U,z.V )
L.O0D    = line: new ( z.O_0,z.D )
z.W      = intersection (L.UV,L.O0D)
z.R      = L.UV: projection (z.O_1)
z.S      = L.UV: projection (z.O_2)
z.O      = C.DC : inversion (z.W)
\end{tkzelements}

\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[teal](O_0,B)
\tkzDrawSemiCircles[thin,teal](O_1,C O_2,B)
\tkzDrawArc[purple,delta=0](D,V)(U)
\tkzDrawCircle[new](O_7,C)
\tkzDrawSegments[thin,purple](A,D D,B C,D U,V C,R C,S)
\tkzDrawSegments[thin,red](O,D A,O O,B)
\tkzDrawPoints(A,B,C,D,O_7,R,S,O_1,O_2,O_0,D,U,V,W)
\tkzDrawSegments[cyan](O_1,R O_2,S C,U U,D) 
\tkzDrawSegments[very thin](A,B)
\tkzMarkRightAngles[size=.4,fill=gray!40,opacity=.4](D,C,A A,D,B)
\tkzMarkRightAngles[size=.4,fill=gray!40,opacity=.4](D,S,C D,W,V O_2,S,U O_1,R,U)
\tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_0 C,D,B D,C,R B,C,S A,R,O_1)
\tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D D,B,C R,C,A O_2,S,B)
\tkzLabelPoints[above](D)
\tkzLabelPoints[above left](R)
\tkzLabelPoints[above right](S)
\tkzLabelPoints[left](V)
\tkzLabelPoints[below](C,O_1,O_2,O_0,O)
\tkzLabelPoints[below left](A)
\tkzLabelPoints[below right](B,U,W,O_7)
\end{tikzpicture}

\end{document}