I don't find the cause of this slowness in this figure, and it seems it does not do it well.
\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{calc,decorations.markings,intersections,fpu,angles,quotes}
\begin{document}
\begin{tikzpicture}
\def\sz{3}
\clip circle (\sz);
\draw[name path=cen] circle (\sz);
\draw[name path=pri] (\sz,0)
node[left] {1} circle (\sz);
\draw[name intersections={of=pri and cen},name path=sec]
(intersection-1)
node[below left] {2} circle (\sz);
\draw[name intersections={of=sec and cen},name path=ter]
(intersection-1)
node[below right] {3} circle (\sz);
\draw[name intersections={of=ter and cen},name path=cua]
(intersection-1)
node[right] {4} circle (\sz);
\draw[name intersections={of=cua and cen},name path=qui]
(intersection-2)
node[above right] {5} circle (\sz);
\draw[name intersections={of=qui and cen},name path=sex]
(intersection-2)
node[above left] {6} circle (\sz);
\end{tikzpicture}
It produces the figure:
I was pursuing this result: