Long cycles in 2-connected triangle-free graphs

Dirac showed that a 2-connected graph of order n with minimum degree delta has circumference at least min{2 delta, n}. We prove that a 2-connected, triangle-free graph G of order n with minimum degree delta either has circumference at least min{4 delta-4, n}, or every longest cycle in G is dominating. This result is best possible in the sense that there exist bipartite graphs with minimum degree d whose longest cycles have length 4 delta - 4, and are not dominating.