Why is a graph $2$-connected if and only if it has an ear decomposition?
Olivia Zamora 
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Why is a graph $2$-connected if and only if it has an ear decomposition?
Reading the book "Introduction to Graph Theory" I have come across the following definition and statement:
why is this statement true ?
Suppose I have a graph $G$ that consist of a cycle $C$ and a path $P$ that share no vertices. Then $G$ has an ear decomposition ? Well, I can decompose $G$ into $P_o = C$ and $P_1 = P$ ? $P_o$ is a cycle and $P$ is an ear of $P_0 \cup P_1$ - $P$ is a maximal path whose interval vertices have degree $2$ in $G$ ? But $G$ is not connected and therefore is $0$-connected and not $2$-connected ?
Picture of the graph I've in mind.
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