`a)ABCD` là hình bình hành 

`=>AB=CD=8cm; AD=BC=12cm`

`E in AB=>EB //// CD`

`=>(EB)/(CD)=(IB)/(IC)=(IB)/(IB+BC)`

`<=>(EB)/8 = 7/(7+12)`

`=>EB=(56)/(19) cm`

`EC^2+EB^2=BC^2<=>EC^2=BC^2-EB^2`

`<=>EC^2=12^2-((56)/(19))^2≈135`

`ED^2=EC^2+CD^2=135+8^2`

`<=>ED^2=199=>ED≈14cm`

`b)∆AHB, ∆ACE` có:

`hat(A)` chung`; hat(AHB)=hat(AEC)=90°`

`=>∆AHB` $\backsim$ `∆ACE` `(g.g)`

`AD //// BC=>hat(FAC)=hat(HCB)`

`hat(AFC)=hat(CHB)=90°`

`=>∆BHC` $\backsim$ `∆CFA` `(g.g)`

`c)∆BHC` $\backsim$ `∆CFA`

`=>(BC)/(CH)=(AC)/(AF)=>BC.AF=AC.CH`

`<=>AD.AF=AC.CH`

`∆AHB` $\backsim$ `∆ACE`

`=>(AB)/(AH)=(AC)/(AE)=>AB.AE=AH.AC`

`=>AB.AE+AD.AF=AC.CH+AC.AH`

`<=>AB.AE+AD.AF=AC.(CH+AH)`

`<=>AB.AE+AD.AF=AC.AC`

`<=>AB.AE+AD.AF=AC^2` (đpcm)