1.∵∠GEA+∠AED=∠ADE+∠AED=90°
∴∠GEA=∠ADE
又∵∠GEA=∠BEF
∴Rt△AEG∽Rt△BEF∽Rt△ADE
∴(AG/AE)=(BF/EB)=(AE/AD)
∵AD=AE+EB
∴(AG/AE)=(-BF/-EB)=(AE/AE+EB)
∴{(AG-BF+AE)/(AE-EB+AE+EB)}=(AG/AE)
{(AG-BF+AE)/(2AE)}=(AG/AE)
AG-BF+AE=2AG
AE=AG+BF
2.∵(AG/AE)=(BF/EB)
AE=AG+BF
又∵ AE=x EB=2-x
∴(AG/x)={BF/(2-x)}
BF=x-AG
∴(AG/x)={(x-AG)/(2-x)}
∴(AG/x)={(AG+x-AG)/(x+2-x)}
∴(AG/x)=(x/2)
∴AG=x²/2
∴y=(AG+AD)DC(1/2)
={(x²/2)+2}×2×(1/2)
=(x²/2)+2
3.过C作ED的垂线交ED于M,过F作AD的垂线交AD
于N
∵∠CDM+∠GDM=∠G+∠GDM=90°
∴Rt△GNF∽Rt△DMC
∴(FG/NF)=(DC/MC)
∴点C到直线DE的距离
MC=(NF×DC)/FG
=2×2÷(5/2)
=8/5