Ho copiato le due tikzpicture e il preambolo in un solo documento e ho compilato senza errori di sorta.
`
\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,arrows,trees,positioning,through,intersections,fadings}
\begin{document}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (6,0);
\coordinate (c) at (9,6);
\draw (a)–(b);
\draw(a)–(c);
\draw (c)–(b);
\node(A)[label=$A$] at (a) {$\bullet$};
\node(B)[label=50:$B$] at (b) {$\bullet$};
\node(C)[label=$C$] at (c) {$\bullet$};
\node(c7) at (c)[draw,circle through=(b)] {};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\coordinate (ac) at (intersection 2 of c7 and a–c);
\node(Ca)[label=$aaaaa$] at (ac) {$\bullet$};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{tikzpicture}
\newpage
\begin{tikzpicture}[scale=0.5]
\coordinate (a) at (0,0);
\coordinate (b) at (6,0);
\coordinate (c) at (9,6);
\node(A)[label=$A$] at (a) {$\bullet$};
\node(B)[label=50:$B$] at (b) {$\bullet$};
\node(C)[label=$C$] at (c) {$\bullet$};
\draw[thick] (a)–(b)–(c)–cycle;
% \node(c1) at (a)[draw,circle through=(b)] {};
% \coordinate(ac) at(intersection 1 of c1 and a–c);
%
% \node(c2) at (ac)[draw,circle through=(b)] {};
% \node(c3) at (b)[draw,circle through=(ac)] {};
% \coordinate(bta) at(intersection 1 of c2 and c3 );
% \node(xx)[label=$C$] at (bta) {$\bullet$};
% \coordinate(bisa) at(intersection 1 of a–bta and b–c);
% \draw (a)–(bisa);
%%%%%%%%%%%%%%%%%%%%%%%%%%% funziona %%%%%%%%%%%%%%%%%%
\node(c4) at (b)[draw,circle through=(a)] {};
\coordinate(bc) at(intersection 1 of c4 and b–c);
\node(xx)[label=$prova$] at (bc) {$\bullet$};
\node(c5) at (bc)[draw,circle through=(a)] {};
\node(c6) at (a)[draw,circle through=(bc)] {};
\coordinate(btb) at(intersection 1 of c5 and c6 );
\node(xx)[label=$prova$] at (btb) {$\bullet$};
\coordinate(bisb) at(intersection 1 of b–btb and a–c);
\draw (b)–(bisb);
%%%%%%%%%%%%%%%%%%%%%%%%%%% funziona %%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% non funziona %%%%%%%%%%%%%%%%%%
\node(c7) at (c)[draw,circle through=(b)] {};
\coordinate(ac) at(intersection 2 of c7 and a–c);
\node(xx)[label=$prova2$] at (ac) {$\bullet$};
%%%%%%%%%%%%%%%%%%%%%%%%%%% non funziona %%%%%%%%%%%%%%%%%%
\end{tikzpicture}
\end{document}
`
[attachment=186]TestTikzBisettrice.pdf[/attachment]
Be’, nella seconda figura ci sono un po’ di cose che si sovrappongono, ma credo che quello sia solo perché si tratta di un file di prova.