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> Let $\alpha:(a,b)\rightarrow\mathbb R^2$ be a regular parametrized plane curve. Assume that there exists $t\_0$, $a<t\_0<b,$ such that the distance $|\alpha (t)|$ from the origin to the trace of $\alpha$ will be a maximum at $t\_0$. Prove that the curvature $k$ of $\alpha$ at $t\_0$ satisfies $k(t\_0)\geq1/|\alpha(t\_0)|$.
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I am confused about how to use the condition "the distance $|\alpha (t)|$ from the origin to the trace of $\alpha$ will be a maximum at $t\_0$". Any suggestions?

Thanks.