  We study analytically and numerically electronic properties of a circular
quantum dot made from AA bilayer graphene. We observe a discrete set of dot
radii for which the low-energy electron states are degenerate with respect to
the layer parity. By analogy with the ``magic angles" in the twisted bilayer
graphene we refer to these radii as ``magic". Such a feature is unique for the
AA structures and is related to a specific layer-symmetry of the AA graphene
bilayer: the parity of the highest occupied level changes from layer-symmetric
to layer-antisymmetric when the radius of the AA dot is equal to its magic
value. We explore an analogy in the electronic structure between twisted
bilayer graphene at the magic twist angle and the AA quantum dot with magic
radius. We argue that this analogy can be helpful for theoretical description
of the electronic properties of the twisted bilayer graphene.
