  We do further investigation in a certain cosine function defined for smooth
Minkowski spaces. We prove that such function is symmetric if and only if the
referred space is Euclidean, and also that it can be given in terms of the
Gateaux derivative of the norm. As an application we use it to study the ratio
between the lengths of tangent segments drawn through an external point to the
unit circle of a Radon plane. We also give an easy characterization of such
planes in terms of signs of the cosine function.
