Let the side length of equilateral △ABC be, and the side length of equilateral △ABC be.

O is the midpoint between BC and EF,

∴AO and DO are the middle vertical lines between BC and EF.

∴∠AOC=∠DOC=900，

∴∠AOD= 1800—∠COE。

∠∠BOE = 1800—∠COE，

∴∠AOD=∠BOE。

A0 and d0 are vertical lines of BC and EF,

Get OB=a/2, OE=b/2, OA=a√3/2, OD= b√3/2.

So OA/OB=(a√3/2)/(a/2)= √3, OD/OE=( b√3/2)/(b/2)=√3.

∴△AOD∽△BOE

∴AD:BE= √3: 1