# Cycle in biconnected graph

Suppose a graph is biconnected and has more than two vertices. Is it true that any two vertices must lie on a cycle?

My idea is: the property of being connected implies that any two vertices $$a,b$$ must be connected by some path. Moreover, if we remove $$a$$ or $$b$$, the graph remains connected. But I'm not sure if it implies that $$a,b$$ must lie on a cycle.

• What if there were two intersecting paths $D,D'$ that intersected $C$ at different vertices? – Shubham Johri Jun 6 at 8:56