∫△ABC and△△△ def are equilateral triangles, and O is the midpoint of BC and EF.

∴AO⊥BC,DO⊥EF,∠EDO=30, ∠ package =30,

∴OD:OE=OA:OB= √3: 1，

∠∠ Doe +∠EOA =∠ Boya +∠EOA means ∠ Doe =∠EOB,

∴△DOA∽△EOB，

∴OD:OE=OA:OB=AD:BE=√3: 1.

So the value of ad: be is √ 3: 1.