如图，AB是⊙O的直径，弦CD⊥AB于点G．点F是CD上一点，且满足$\frac{CF}{FD}$=$\frac{1}{3}$，连接AF并延长交⊙0于点E．连接AD、DE，若CF=2，AF=3．给出下列结论：

①△ADF∽△AED；

②FG=2；

③tan∠E=$\frac{\sqrt{5}}{2}$；

④S_△DEF=4$\sqrt{5}$．

其中正确的是（　　）

    In our school, we have four classes in the morning. From nine forty to ten o'clock, we can have a twenty-minute rest time. It is a quarter to ten now. Look! Most of us are going out of the classroom. Some boys are playing basketball, soccer or running on the playground. Some girls are watching them or playing badminton. There are also some students in the classroom. They are talking. A few of them are reading or doing homework. Look! A girl is looking at the birds in a tree from the window. She is smiling.

    What are our teachers doing? They are either working or talking to the students in the office. They are all very busy but happy!

）如图，菱形ABCD的对角线的长分别为2和5，P是对角线AC上任一点（点P不与点A、C重合）且PE∥BC交AB于E，PF∥CD交AD于F，则阴影部分的面积是（　　）