4.
如图,点E是正方形ABCD的边BC延长线一点,连接AE交CD于F,作∠AEG=∠AEB,EG交CD的延长线于G,连接AG,当CE=BC=2时,作FH⊥AG于H,连接DH,则DH的长为( )
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| A. | 2-$\sqrt{2}$ | B. | $\sqrt{2}-1$ | C. | $\frac{\sqrt{2}}{2}$ | D. | $\frac{2}{3}$ |