\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);

numeric u; u = 144;

path base; base = fullcircle rotated 180 scaled u;
numeric s; s = 1/8;

pair A; A = point 0 of base;
path cardioid; cardioid = for t = 0 step s until length base:
  A reflectedabout(precontrol t of base, postcontrol t of base) ..
endfor cycle;

numeric t; t = 5.4;
pair A, M, P, P', Q, Q', R;
A = point 0 of base;
Q  = point t of base;
Q' = point t-4 of base;
P = A reflectedabout(precontrol t of base, postcontrol t of base);
P' = A reflectedabout(precontrol t-4 of base, postcontrol t-4 of base);
M = 1/2[P, P'];
R = whatever[P, Q] = whatever[P', Q'];

%draw Q' -- R -- Q withcolor 3/4;
draw 3[postcontrol t of base, precontrol t of base]
  -- 5[precontrol t of base, postcontrol t of base] withcolor 3/4;  
%draw 5[postcontrol t-4 of base, precontrol t-4 of base]
%  -- 3[precontrol t-4 of base, postcontrol t-4 of base] withcolor 3/4;  

draw fullcircle scaled 2 abs (Q-A) shifted Q withcolor 7/8;

%
%draw P' -- Q' -- Q -- P -- cycle;
draw A -- Q -- P -- cycle;

draw base withcolor 2/3 blue;
draw origin withpen pencircle scaled dotlabeldiam withcolor 2/3 blue;
draw cardioid withcolor 1/4[white, 1/2 red];

dotlabel.ulft("$A$", A);
%dotlabel.ulft("$M$", M);
dotlabel.top ("$P$", P);
%dotlabel.llft("$P'$", P');
dotlabel.urt ("$Q$", Q);
%dotlabel.bot ("$Q'$", Q');
%dotlabel.lrt ("$R$", R);

endfig;
\end{mplibcode}
\end{document}