∴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.