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直线与圆的交点

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直线与圆的交点

为什么这个例子只起到部分作用？

\documentclass{minimal}
\usepackage{etex}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,arrows,trees,positioning,through,intersections,fadings}
\begin{document}
    \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);
%%%%%%%%%%%%%%%%%%%%%%%%%%% work %%%%%%%%%%%%%%%%%%
        \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);
%%%%%%%%%%%%%%%%%%%%%%%%%%% work %%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% it doesn't work%%%%%%%%%%%%%%%%%%
\node(c7) at (c)[draw,circle through=(b)] {};
\coordinate(ac) at(intersection 2 of c7 and a--c);
\node(xx)[label=$prova2$] at (ac) {$\bullet$};
%%%%%%%%%%%%%%%%%%%%%%%%%%% it doesn't work %%%%%%%%%%%%%%%%%%

\end{tikzpicture}
\end{document}

答案1

首先，我认为最好使用带有等的新语法path name，name intersections就像在 Euclide 的 pgf 2.1 教程中一样。

(c)--(a)而不是(a)--(c)解决问题。

\documentclass{minimal}
\usepackage{etex}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,arrows,through,intersections}
\begin{document}
\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;
%%%%%%%%%%%%%%%%%%%%%%%%%%% work %%%%%%%%%%%%%%%%%%
            \node(c4) at (b) [draw,circle through=(a)] {};
            \coordinate(bc) at (intersection 1 of c4 and b--c);
            \node(xx) at (bc) {\color{red}$\bullet$};
            \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) at (btb) {\color{green}$\bullet$};
            \node(bisb) at (intersection 1 of b--btb and a--c){\color{blue}$\bullet$};
            \draw[dashed] (b)--(bisb);     
%%%%%%%%%%%%%%%%%%%%%%%%%%% work %%%%%%%%%%%%%%%%%%
\node(c7) at (c)[draw,circle through=(b)] {};
\coordinate(ac) at (intersection 1 of c7 and c--a);
\node(xx) at (ac) {\color{orange}$\bullet$};

\end{tikzpicture}
\end{document}

在此处输入图片描述

更新

使用更新的语法，代码变为

\documentclass{minimal}
\usepackage{etex}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,arrows,through,intersections}
\begin{document}
\begin{tikzpicture}[scale=0.5]
  \tikzset{mark coordinate/.style={inner sep=0pt,
                                   outer sep=0pt,
                                   minimum size=3pt,
                                   fill=#1,
                                   circle}
                                   }
  \draw[thick] (0,0)  coordinate [mark coordinate=black,label=$A$]      (a) --
               (6,0)  coordinate [mark coordinate=black,label=50:$B$]   (b) --
               (9,6)  coordinate [mark coordinate=black,label=$C$]      (c) -- cycle ; 

  \node [name path=Circle1,draw,circle through=(a)] at (b) {};
  \path [name path=BC] (b) -- (c); 
  \path [name intersections={of=BC and Circle1, name=i}] 
        (i-1) coordinate [mark coordinate=red];
  \node [name path=Circle2,draw,circle through=(a)]   at (i-1)   {};
  \node [name path=Circle3,draw,circle through=(i-1)] at (a)     {};
  \fill [name intersections={of=Circle2 and Circle3, name=j}] 
        (j-1) coordinate [mark coordinate=green];
  \path [name path=AC]   (a) -- (c);
  \path [name path=Bj-1] (b) -- (j-1);
  \fill [name intersections={of=Bj-1 and AC, name=k}] 
        (k-1) coordinate [mark coordinate=blue];
  \draw [red] (b)--(k-1);      
  \node [name path=Circle4,draw,circle through=(b)] at (c)  {};
  \fill [name intersections={of=Circle4 and AC, name=l}] 
        (l-1) coordinate [mark coordinate=orange];    
\end{tikzpicture}
\end{document}

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