∫OE is the bisector of ∞∠AOB, EC⊥OA, ED⊥OB,

∴EC=ED

△ ced is an isosceles triangle,

∴∠EDC=∠ECD

(2)OC and OD are equal.

∵EC⊥OA,ED⊥OB，

∴∠ODE=∠OCE=90

In Rt△ODE and Rt△OCE, OE=OE and DE=CE.

∴Rt△ODE≌Rt△OCE(HL)

∴OD=OC

(3)OE is the median vertical line of the line segment CD.

EC = ED，

∴ point e is on the perpendicular bisector of the line segment CD.

OC = OD，

∴O point is on the perpendicular bisector of the line segment CD,

OE is the perpendicular bisector of the line segment CD.