So arc AC= arc BC

Therefore, AC=BC ∠AOC=∠COB (in the same circle or the same circle, if the quantities of ① two central angles, ② two arcs and ③ two chords are the same, the quantities of their corresponding other groups are equal respectively).

∠ AOB = 120。

So ∠ AOC = ∠ COB = 60, and the large angle ∠ AOB = 240.

So ∠ ACB = 120 (in the same circle or equal circle, the circumferential angle of the same arc or chord is equal to half the central angle).

CO = co again

So △AOC=△BOC (corner edge)

So ∠OAC=∠CBO=60

So △AOC and △BOC are equilateral triangles.

So AO=BO=AC=BC

So the quadrangle OACB is a diamond.