First of all, we can easily get that OCA has RT△, and then because we know the slave coordinates of C, we can get this RT△ side length.

Then the length of CB=BD can be known from the cosine formula of ∠CAB= 120, AB=4 and CA.

Then CD=OD-CO is obtained from the sine formula of COA=60, OB=OA+AB and DB.

Finally AC=DC.