Row Rank Equals Column Rank

Hence a butterfly inscribed in a quadrilateral satisfies the same relation (1) as a butterfly inscribed in a circle. Equivalently, the conclusion of the theorem indicates that the ratio of the ratios, (AM/IM)/(CN/IN), is the same as the ratio IA/IC, or that the harmonic mean of IC and IM equals the harmonic mean of IA and IN. In either case, if IC = IA, we have IM = IN thereby the analog of the usual butterfly theorem for quadrilaterals.