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20 12 Guangzhou Mathematics Final Exam Answers
(2) Take the midpoint g of BC and connect FG to EC, H and EG.

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