Cycles through 4 vertices in 3-connected graphs

S.C. Locke proposed a question: If GG is a 3-connected graph with minimum degree dd and XX is a set of 4 vertices on a cycle in GG, must GG have a cycle through XX with length at least min{2d,|V(G)|}min{2d,|V(G)|}? In this paper, we answer this question.