Walks, Paths and Connectivity · Medium problem

A $6$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}1$ has an extra chain of vertices $7,8,9$ hanging off vertex $1$ (edges $12,23,34,45,56,61,17,78,89$). If the bridge $89$ is removed, what are the sizes of the two resulting pieces? Give the smaller one.