如图正方形ABCD的边长为4，点E是AB上的一点，将△BCE沿CE折叠至△FCE，若CF，CE恰好与以正方形ABCD的中心为圆心的⊙O相切，则折痕CE的长为（    ）

阅读下列古诗答题。

                                                                                                                                       《绝句》
                                                                                                                                          唐·杜甫
                                                                                                                           迟日江山丽，春风花草香。
                                                                                                                           泥融飞燕子，沙暖睡鸳鸯。
       【注释】泥融：指冻泥融化，又软又湿。