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tikz 线延长时的交点

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tikz 线延长时的交点

我有一条被圆包围的短线，想找到这条线与圆延伸的交点。

下面的代码是我的 MWE。我认为错误是由于没有找到交点而导致的，因为作为线段，该线不与圆相交。那么如何才能最好地解决这个问题呢？

以下是我目前所掌握的信息：

\documentclass{article}


\usepackage{tikz}
\usetikzlibrary{through}
\usetikzlibrary{intersections}


\begin{document}
\begin{tikzpicture}
\coordinate (X) at (0,0);
\coordinate (A) at (1,1);
\coordinate (B) at (2,2);
\coordinate (C) at (3,0);

\draw (A) -- (B);
\draw[name path=AB] (A)--(B);

\node[draw,name path=K1] at (X) [circle through=(C)]{};
\path [name intersections={of=K1 and AB}];

\coordinate [label=above:$D$] (D) at (intersection-1);
\coordinate [label=above:$E$] (E) at (intersection-2);

\end{tikzpicture}
    
\end{document}

答案1

您可以不绘制线而直接延长线。最简单的方法是使用calc库。该overlay选项表示路径不会添加到图片大小中。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{through} 
\usetikzlibrary{intersections,calc} 
\begin{document} 
\begin{tikzpicture} 
\coordinate (X) at (0,0); 
\coordinate (A) at (1,1); 
\coordinate (B) at (2,2); 
\coordinate (C) at (3,0); 
\draw (A) -- (B); 
\path[overlay,name path=AB] ($(B)!10cm!(A)$)--($(A)!10cm!(B)$); 
\node[draw,name path=K1] at (X) [circle through=(C)]{};
\path [name intersections={of=K1 and AB}]
(intersection-1) coordinate [label=above:$D$] (D)
(intersection-2) coordinate [label=above:$E$] (E); 
\end{tikzpicture} 
\end{document}

线与圆的交点

答案2

在此处输入图片描述

\documentclass{article}


\usepackage{tikz}
\usetikzlibrary{through}
\usetikzlibrary{intersections}


\begin{document}
\begin{tikzpicture}
\coordinate [label=x](X) at (0,0);
\coordinate [label=a](A) at (-4,-4);
\coordinate [label=b](B) at (3,3);
\coordinate [label=c](C) at (3,0);

\draw (A) -- (B);
\draw[name path=AB] (A)--(B);

\node[draw,name path=K1] at (X) [circle through=(C)]{};
\path [name intersections={of=K1 and AB}];

\coordinate [label=above:$D$] (D) at (intersection-1);
\coordinate [label=above:$E$] (E) at (intersection-2);

\end{tikzpicture}
    
\end{document}

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