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一道几何概型问题

本帖最后由 青青子衿 于 2017-3-10 12:21 编辑

正方形\(ABCD\)外切于圆\(O\),在正方形\(ABCD\)内随机取两点\(E\)、\(F\),线段\(EF\)与圆\(O\)相交的概率为?
QQ截图20170310121924.png
2017-3-10 12:20

tikz码:
  1. \documentclass{article}
  2. \usepackage{tikz}
  3. \usetikzlibrary{intersections,calc,through}
  4. \begin{document}
  5. \begin{tikzpicture}
  6. [dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
  7.   extended line/.style={shorten >=-#1,shorten <=-#1},
  8.   extended line/.default=3cm]
  9. \coordinate [label=below:$O$] (O) at (3,3);
  10. \fill(O) circle (1.5pt);
  11. \coordinate [label=above left:$A$] (A) at (0,6);
  12. \fill(A) circle (1.5pt);
  13. \coordinate [label=above right:$B$] (B) at (6,6);
  14. \fill(B) circle (1.5pt);
  15. \coordinate [label=below right:$C$] (C) at (6,0);
  16. \fill(C) circle (1.5pt);
  17. \coordinate [label=below left:$D$] (D) at (0,0);
  18. \fill(D) circle (1.5pt);
  19. \coordinate [label=below left:$E_1$] (E) at (4.4,5.8);
  20. \fill(E) circle (1.5pt);
  21. \coordinate [label=below left:$F_1$] (F) at (5.9,4.1);
  22. \fill(F) circle (1.5pt);
  23. \draw[red] [name path=EF] (E) -- (F);
  24. \draw [name path=Cir] (3,3)circle(3);
  25. \path [name intersections={of = Cir and EF}];
  26. \coordinate[label=right:$P_1$] (P)  at (intersection-1);
  27. \fill(P) circle (1pt);
  28. \coordinate[label=left:$Q_1$] (Q)  at (intersection-2);
  29. \fill(Q) circle (1pt);
  30. \draw(0,0)rectangle(6,6);
  31. \node [dot=above right:$E_2$] (J) at (0.55,1) {};
  32. \node [dot=right:$F_2$] (K) at (0.32,0.3) {};
  33. \draw [red] (J) -- (K);
  34. \draw [style=dashed] (J) -- ($(K)!5.0cm!(J)$);
  35. \draw [style=dashed,extended line=1.0cm] ($(J)!(O)!(K)$) -- (O);
  36. \fill [red] ($(J)!(O)!(K)$) circle [radius=2pt];
  37. \end{tikzpicture}
  38. \end{document}
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我来看tikz代码。。

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