Show any two edges in a 2-connected graph lie on a cycle So I found some proofs on any two vertices would lie on a cycle, but stuck on dealing with edges. We can say any two edges are connected, but does that just imply they will be on a common cycle? 

Although this question is already a few months old, I will post my (hopefully working) answer, as I was searching for it for a long time as well.
We can extend the graph G by adding two vertices a, b in the middle of the edges wanted in one cycle. This does not change our graph being 2-connected, but now we can reduce the question of finding a cycle containing the two edges in G to the question of a cycle containing a and b in G'.
