The lasing spectra and threshold values of material gain for the dipole-type supermodes of an active microdisk concentrically coupled with an external passive microring are investigated. TE polarized modes are treated accurately using the linear electromagnetic formalism of the 2-D lasing eigenvalue problem (LEP) with exact boundary and radiation conditions. The influence of the microring on the lasing frequencies and thresholds is studied numerically, demonstrating threshold reduction opportunities. This is explained through the analysis of the mode near-field patterns and the degree of their overlap with the active region, as suggested by the optical theorem applied to the LEP solutions.