ARO-quasigroups

In this paper the concept of ARO-quasigroup is introduced and some identities which are valid in a general ARO-quasigroup are proved. The "geometric" concepts of midpoint, parallelogram and affine-regular octagon is introduced in a general ARO-quasigroup. The geometric interpretation of some proved identities and introduced concepts is given in the quasigroup $C(1+\sqrt2/2)$.