We investigate the positions of stable circular massive particle orbits in the Majumdar--Papapetrou dihole spacetime with equal mass. In terms of qualitative differences of their sequences, we classify the dihole separation into five ranges and find four critical values as the boundaries. When the separation is relatively large, the sequence on the symmetric plane bifurcates, and furthermore, they extend to each innermost stable circular orbit in the vicinity of each black hole. In a certain separation range, the sequence on the symmetric plane separates into two parts. On the basis of this phenomenon, we discuss the formation of double accretion disks with a common center. Finally, we clarify the dependence of the radii of marginally stable circular orbits and innermost stable circular orbits on the separation parameter. We find a discontinuous transition of the innermost stable circular orbit radius. We also find the separation range at which the radius of the innermost stable circular orbit can be smaller than that of the stable circular photon orbit.
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