As shown in the figure: in ladder ABCD, ad is parallel to BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB (1) Find out all the similar triangles in the graph and prove them (2) Let BD = x, be = y, find out the function analytic expression of Y and X (3) When ad = 4, find the length of be

As shown in the figure: in ladder ABCD, ad is parallel to BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB (1) Find out all the similar triangles in the graph and prove them (2) Let BD = x, be = y, find out the function analytic expression of Y and X (3) When ad = 4, find the length of be

(1) In ∵ ladder ABCD, ad ∥ BC, ab = CD = 2
∴∠BAD＝∠CDA＝∠BDA+∠BDC
∠BEC＝∠ECD+∠BDC
∴∠BAD＝∠BEC
∠BDA＝∠EBC
∴△ABD∽△ECB
∵∠DCE=∠ADB
∴∠DCE=∠DBC
∠BDC＝∠CDE
∴△BCD∽△CED
(2) Let BD = x be = y
∵△BCD∽△CED
∴BD/CD=CD/DE
x/2=2/(x-y)
x²-xy=4
y=(x²-4)/x,（x>0）
(3)∵BC=6,AD=4
Do DF ⊥ BC through D and cross BC to F
∴CF＝1,DF＝√3,BD＝√(3+25)=2√7
∵y=(x^2-4)/x,
∴BE=(28-4)/(2√7)=12√7/7