∴ad//bc；

∴∠dab+∠abc= 180；

∠DAB:∠ABC = 1:2；

∴∠dab=60； ∠ABC = 120；

∵ABCD is diamond;

∴AB=BC=CD=AD= perimeter/4 =16/4 = 4;

△ Abd is an equilateral triangle;

∴bd=ab=4；

∵ABCD is diamond;

∴bd⊥ac；

∴OA=OC= root number 3/2AB=2 root number 3;

Root number 3 of AC=2OA=4