Wie kann ich einen vollständigen Kreis mit Beschriftungen um den Kreis herum erhalten?

Question

Ich habe diesen Halbkreis zur Veranschaulichung und ich brauche die beiden Münder, um einander zu berühren, wie genau ein Kreis, immer noch mit metrischer Beschriftung, wie ich sie in derMWE

% !TeX program = lualatex
\documentclass[a4paper,14pt]{extarticle}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} 
\usepackage{amssymb,amsfonts,amsmath,graphicx,autobreak}
\usepackage{changepage,mathtools,amsthm,tikz,blindtext}
\usepackage{inputenc,float,caption,subcaption,enumitem}
\usepackage[font=large,labelfont=bf,font=normalfont,labelsep=colon]{caption}
\usepackage[font=small,labelfont=bf,font=bf,labelsep=colon]{subcaption}
\usepackage{csquotes} %for single quoatation mark
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%for arc and angles
\usetikzlibrary{calc, angles}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{luatex85}
\usepackage{luamplib}
\begin{document}
    \begin{figure}[H]
    \mplibtextextlabel{enable}
    \begin{mplibcode}
        beginfig(1);
        path C, C'; 
        C = subpath(2,0) of fullcircle rotated 45 scaled 640;
        C' = C scaled 1.02;
        numeric p[];
        p1    = 1/8;
        p2    = 2/8;
        p3    = 3/8;
        p.t   = 5/8;
        p.tt  = 6/8;
        p.ttt = 7/8;
        p.n   = 9/8;
        p.l  = 10/8;
        p.zz = 13/8;
        for t=  1/64 step 1/64 until   3/64: drawdot point t of C' withpen pencircle scaled 1; endfor
        for t= 29/64 step 1/64 until  35/64: drawdot point t of C' withpen pencircle scaled 1; endfor
        for t= 61/64 step 1/64 until  67/64: drawdot point t of C' withpen pencircle scaled 1; endfor
        for t= 89/64 step 1/64 until  95/64: drawdot point t of C' withpen pencircle scaled 1; endfor
        for t=116/64 step 1/64 until 119/64: drawdot point t of C' withpen pencircle scaled 1; endfor
    
        forsuffixes $=1,2,3,t,tt,ttt,n,l,zz:
        draw point p$ of C -- point p$ of C' withcolor 2/3 blue;
        label.top("$x_{" & 
            if     str $ = "tt" : "t+1" 
            elseif str $ = "ttt": "t+2" 
            elseif str $ = "zz" : "n+l-1" 
            else: str $ fi
            & "}$", point 1 of C') rotated (45-45*p$);
        endfor
    
            draw C;
    
        vardef mark(suffix a, b)(expr s, T) =
        save arc; path arc;
        arc = subpath(p.a, p.b) of C scaled s;
        interim ahangle  := 180; interim ahlength := 5;
        drawdblarrow arc withcolor 2/3 green;
    
        save pp; picture pp; 
        pp = thelabel(T rotated angle direction 1/2 of arc, point 1/2 of arc);
        unfill bbox pp; draw pp;
        enddef;
    
        mark(1, t, 0.95, textext("$B_1$"));
        mark(2, tt, 0.90, textext("$B_2$"));
        mark(3, ttt, 0.85, textext("$B_3$"));
        mark(n, zz, 0.95, textext("$B_k$"));
    
        endfig;
    \end{mplibcode}
    \caption{Circular Block Bootstrap}
    \label{fig5}
\end{figure}

\end{document}