一道几何概型问题

青青子衿

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？

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}

复制代码

isee

我来看tikz代码。。