Arbelos

In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the baseline) that contains their diameters.(Wikipedia)

Example 1 Bankoff's circle

In geometry, the Bankoff circle or Bankoff triplet circle is a certain Archimedean circle that can be constructed from an arbelos; an Archimedean circle is any circle with area equal to each of Archimedes' twin circles. The Bankoff circle was first constructed by Leon Bankoff in 1974.(Wikipedia)

[PDF] [TEX]

\documentclass{standalone}
\usepackage{tkz-euclide}
\tkzSetUpColors[background=white,text=teal]  
\tkzSetUpPoint[size=2,color=teal]
\tkzSetUpLine[thin,color=teal]
\tkzSetUpCompass[color=orange,ultra thin,/tkzcompass/delta=10]
\tikzset{label style/.style={color=teal,font=\footnotesize}}
\begin{document}
  \begin{tikzpicture}
  \tkzDefPoints{0/0/A,12/0/C}
  \tkzDefGoldenRatio(A,C)                          \tkzGetPoint{B}
  \tkzDefMidPoint(A,C)                             \tkzGetPoint{O_1}
  \tkzDrawSemiCircles[teal](O_1,C)
  \tkzDefMidPoint(A,B)                             \tkzGetPoint{O_2}
  \tkzDefMidPoint(B,C)                             \tkzGetPoint{O_3}
  \tkzDefPointBy[rotation=center O_3 angle 90](C)  \tkzGetPoint{P}
  \tkzDefPointBy[rotation=center O_2 angle 90](B)  \tkzGetPoint{Q}
  \tkzDefIntSimilitudeCenter(O_1,A)(O_2,A)         \tkzGetPoint{I_1}
  \tkzDefIntSimilitudeCenter(O_1,A)(O_3,B)         \tkzGetPoint{I_2} 
  \tkzInterLL(C,Q)(A,P)                            \tkzGetPoint{S}
  \tkzInterLC(B,S)(O_1,A)                          \tkzGetSecondPoint{Z}
  \tkzInterCC(I_1,A)(O_3,C)                        \tkzGetFirstPoint{Y}
  \tkzInterCC(I_2,C)(O_2,A)                        \tkzGetSecondPoint{X}
  \tkzDefCircle[circum](X,Y,Z)                     \tkzGetPoint{O_4}
  \tkzDefCircle[circum](B,Y,X)                     \tkzGetPoint{O_5}        
  \tkzDrawSemiCircles[fill=teal!10,opacity=.2,teal](O_2,B O_3,C)
  \tkzDrawCircle[fill=purple!30,opacity=.3](O_5,B)
  \tkzDrawSemiCircles[gray](I_2,C)
  \tkzDrawSemiCircles[gray,swap](I_1,A) 
  \tkzDrawCircle[fill=orange!20,opacity=.2](O_4,Z)
  \tkzDrawSegment(A,C)
  \tkzDrawPoints(A,B,C,Z,X,Y,I_1,I_2,O_1,O_2,O_5,O_3,O_4)
  \tkzLabelPoints[below](A,B,C,I_1,I_2,O_2,O_3,O_1)
  \tkzLabelPoints[above](Z,O_5,O_4)
  \tkzLabelPoints[right](Y)
  \tkzLabelPoints[left](X)
\end{tikzpicture}
\end{document}