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From the gravitational structure equations of an anisotropic and spherically symmetric star in the presence of a cosmological constant, we derive the inequality which limits the mass-radius ratio, imposing energy conditions on the matter. From this inequality, we display how the cosmological constant modifies the Buchdahl limit,and express the bounds on both the mass-radius ratio and surface redshift in terms of the ratio between the cosmological constant and mean energy density of the star.