I drew a circle for [Pappus chain](http://mathworld.wolfram.com/PappusChain.html) on an arbelos. How to draw other circles?

[![enter image description here](https://i.stack.imgur.com/RMtfa.jpg)](https://i.stack.imgur.com/RMtfa.jpg)

```
\documentclass[10pt]{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage[x11names]{xcolor}
\usepackage{fouriernc}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}

\begin{document}

\centering

\begin{tikzpicture}[scale=1.5,line join=round,font=\small]
\coordinate[label=below:$A$] (A) at (0,0);
\coordinate[label=below:$B$] (B) at (4,0);
\coordinate[label=below:$C$] (C) at (6,0);
\draw[thick,lightgray](0,0)--(6,0);
\draw[Burlywood4,thick] 
(6,0) arc [radius=3, start angle=0, delta angle=180] -- 
(0,0) arc [radius=2, start angle=180, delta angle=-180]--(4,0) arc [radius=1, start angle=-180, delta angle=-180]--cycle;

\path[name path=b1] 
(6,0) arc [radius=3, start angle=0, delta angle=180];
\path[name path=b2] (0,0) arc [radius=2, start angle=180, delta angle=-180];
\path[name path=b3] (4,0) arc [radius=1, start angle=-180, delta angle=-180];

\draw[olive!50,name path=b4] (4,0) arc (225:60:{sqrt(2)});
\draw[violet!50,name path=b5] (4,4) arc (45:-40:{2*sqrt(2)});
\path [name intersections={of = b4 and b5, by={D}}];
\path [name intersections={of = b2 and b4, by={T,E}}];
\path [name intersections={of = b3 and b5, by={F}}];
\coordinate (K) at ($(E)!.5!(F)$);
\coordinate (L) at ($(D)!.5!(F)$);
\coordinate (M) at ($(K)!1cm!90:(F)$);
\coordinate (N) at ($(L)!1cm!90:(D)$);
\path[name path=g1] (K)--(M);
\path[name path=g2] (L)--(N);
\path [name intersections={of = g1 and g2, by={O}}];
\draw[thick,Red4]
  let 
  \p1=( $(E)-(O) $ )
  in
  (O) circle ({veclen(\x1,\y1)});
\foreach \p in {D,E,F,O}
\draw[fill,DodgerBlue4] (\p) circle(1pt);
%\foreach \p in {D,E,F}
%\node[above] at (\p) {$\p$};
\end{tikzpicture}
\end{document}

```