∴OA=BA=OB，

△ AOB is an equilateral triangle,

∴∠AOB=60，

A, according to the theorem of the circle angle: ∠ BAC =12 ∠ BOC =14 ∠ Bao =14× 60 =15, so this option is correct;

B, ∵OC⊥AB, OC is the radius,

∴ Arc AC= Arc BC, so this option is wrong;

c、OA = OB，OA=AB，

∴OA=OB=AB，

∴△ABO is an equilateral triangle, ∠ AOB = 60, AB can form a regular hexagon, so this option is wrong;

D, because OC⊥AB according to the vertical diameter theorem, arc AC= arc BC, and according to the conclusion in A, the length of chord AC is equal to the side length of the inscribed circle of a regular dodecagon, so this option is wrong;

So choose a.