DE-BUNDESWETTBEWERB 2010 Problem 5

Let $a, b, c$ be the side lengths of an non-degenerate triangle with $a \le b \le c$ . With $t (a, b, c)$ denote the minimum of the quotients $\frac{b}{a}$ and $\frac{c}{b}$ . Find all values that $t (a, b, c)$ can take.