如何定义两条线段AD与BC延长线的交点 F ?

%MWE如下:
%----如何定义两条线段AD与BC延长线的交点 F ?
%
%----xelatex编译
\documentclass{article}
\usepackage{xeCJK}%使用xeCJK中文处理宏包
\usepackage{amsmath,amssymb,bm}%ams数学符号
\usepackage{tikz}
\usetikzlibrary{arrows,intersections}
\usetikzlibrary{positioning,backgrounds}
\usetikzlibrary{fadings}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usetikzlibrary{shadings}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usepackage{verbatim}
\begin{document}
\begin{tikzpicture}[scale=1.5,line width=0.75pt]
          %点A
          \coordinate (A) at (-1,0);
          \node[left] at (A) {$A$};
          %点D
          \coordinate (D) at ([shift=(50:1.2cm)]A);
          \node[left] at (D) {$D$};
         
          %点B
          \coordinate (B) at (1,0);
          \node[left] at (B) {$B$};
          %点C
          \coordinate (C) at ([shift=(110:1.2cm)]B);
          \node[right] at (C) {$C$};
 
%失败尝试--定义直线AD与BC交点F
          \coordinate (F1) at ($(A)!2!0:(D)$);
          \coordinate (F2) at ($(B)!2!0:(C)$);
          \path[name path=x] (A)--(F1);
          \path[name path=y] (B)--(F2);
          \path[name intersections={of=x and y, name=i}] coordinate (F);
          \node[above] at (F) {$F$};
%失败尝试--定义直线AD与BC交点F
 
         
          %连线FAB
          \draw (F)--(A)--(B)--cycle;
        \end{tikzpicture}
\end{document}


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失败的运行效果图如下:
018b47e72cc23ec

 
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