Q:  Stars in the red clump have an absolute magnitude of M_I = -0.23.
          What is the distance to the SMC?


            The apparent magnitude in I-band, based on these figures,
            is about

                  m_I  =  18.4


            Therefore, the distance modulus is

                 (m - M)  =  18.4 - ( -0.23 )  =  18.6

            and

                           0.2 * ( m-M  + 5 )
                   d  =  10

                           0.2 * ( 23.6 )          4.72
                      =  10                  =   10         pc

                     
                      =  52,000 pc



          What is the distance to the LMC?


            The apparent magnitude in I-band, based on these figures,
            is about

                  m_I  =  18.2


            Therefore, the distance modulus is

                 (m - M)  =  18.2 - ( -0.23 )  =  18.4

            and

                           0.2 * ( m-M  + 5 )
                   d  =  10

                           0.2 * ( 23.4 )          4.68
                      =  10                  =   10         pc


                      =  48,000 pc



      (More careful distance calculations take into account additional
          factors and find slightly different distances)