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