Circumference and girth

Let G be 2-connected graph with girth g and minimum degree d. Then each pair of vertices of G is joined by a path of length at least max{1/2(d ? 1)g, (d ? 3/2)(g ? 4) + 2} if g ? 4, and the length of a longest cycle of G is at least max{[(d ? 1)(g ? 2) + 2], [(2d ? 3)(g ? 4) + 4]}.