FDCD is a diamond.

∴∠DFC=∠GFC

∠∠CGH =∠CEB = 90°∴fg is the middle vertical line of EC.

∴∠GFE=∠GFC

∠∠AEF =∠GFE

∴∠AFE=∠GFE=∠GFC=∠DFC

∴∠EFD=3∠AFE

∴k=3

(3) Let GH=x, then BE=2x.

CE？ = 10? -(2x)？ = 100-4x？ ，CF？ =FH？ +CH？ =(5-x)？ +5? -x？ =50- 10x

CE？ -CF？ =50-4x？ + 10x

When x=- 10/2×(-4)=5/4, there is a maximum value, and FH=5-x= 15/4, and CH=√5? -(5/4)? =5√ 15/4

∴tan∠fcd=tan∠gfc=ch/fh=√ 15/3