如图，矩形ABCD中，E是BC上一点，连接AE，将矩形沿AE翻折，使点B落在CD边F处，连接AF，在AF上取点O，以O为圆心，OF长为半径作⊙O与AD相切于点P．若AB=6，BC=3 $\sqrt{3}$ ，则下列结论：①F是CD的中点；②⊙O的半径是2；③AE= $\frac{9}{2}$ CE；④S_阴影= $\frac{\sqrt{3}}{2}$ ．其中正确结论的序号是____．

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                                                                                                         冷香菊
                                                                                                         陈荣卿
                                                                                       晚秋风紧晓霜寒，香阵飘飘透竹帘。
                                                                                       荒径幽林甘冷落，肯于人世学趋炎？