In trapezoid ABCD, ab ‖ CD, ∠ ABC = 90 °, ab = 5, BC = 10, Tan ∠ ADC = 2. (1) find the length of DC; (2) e is a point inside the trapezoid, f is a point outside the trapezoid, if BF = De, ∠ FBC = ∠ CDE, try to judge the shape of △ ECF, and explain the reason. (3) under the condition of (2), if be ⊥ EC, be: EC = 4:3, find the length of de

In trapezoid ABCD, ab ‖ CD, ∠ ABC = 90 °, ab = 5, BC = 10, Tan ∠ ADC = 2. (1) find the length of DC; (2) e is a point inside the trapezoid, f is a point outside the trapezoid, if BF = De, ∠ FBC = ∠ CDE, try to judge the shape of △ ECF, and explain the reason. (3) under the condition of (2), if be ⊥ EC, be: EC = 4:3, find the length of de

(1) Through point a, make Ag ⊥ DC, perpendicular foot g, ∵ ab ∥ CD, ∵ BCD = ∠ ABC = 90 °, quadrangle ABCG is rectangular, ∵ CG = AB = 5, Ag = BC = 10, ∵ Tan ∵ ADG = agdg = 2, ∵ DG = 5, ∵ DC = DG + CG = 10; (2) ∵ de = BF, ∵ FBC = ∠ CDE, BC = DC, ≌ Dec ≌ BFC, ≌ EC = CF