Do Carmo's book on "Differential geometry of curves and surfaces" has a problem that I can't find the answer of. It is on page 5(1st exercise problem#2) is:

Let $\displaystyle \alpha(t)$ be a parametrized curve which does not pass through the origin. If $\displaystyle \alpha(t_0)$ is the point of the trace of $\displaystyle \alpha$ closest to the origin

and $\displaystyle \alpha'(t_0) \neq 0$, show that the position vector $\displaystyle \alpha(t_0)$ is orthogonal to $\displaystyle \alpha'(t_0)$.

Here $\displaystyle \alpha'(t_0)$ is the derivative of $\displaystyle \alpha(t)$ at $\displaystyle t_0$.

How do I prove this? Is it possible to give some hints?