AF = a/2 = BF = CE = BE = AD = BD
OF = EO = DO = radius of incircle
angles AFO = OFC = OEC = OEB = ODA = ODB = 90 deg
Hence all these triangles OAD, OBD, OEB, OEC, OFC, OFA are equal.
so angles at O, angle AOF, FOC, COE, EOB, BOD, DOA are all equal.
hence, the angles at O, AOB, BOC, COA are all equal and will be equal to 360 / 3 = 120 deg.