Let $\alpha:(a,b)\rightarrow\mathbb R^2$ be a regular parametrized plane curve. Assume that there exists $t_0$, $a
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 $k(t_0)\geq1/|\alpha(t_0)|$.
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.