DE-BUNDESWETTBEWERB 2025 Problem 6

Determine all real numbers $t$ with $0<t<1$ for which the following statement is true: If, in an acute-angled triangle, the sides with lengths $a$ , $b$ , and $c$ are opposite the angles with sizes $\alpha$ , $\beta$ , and $\gamma$ , as usual, and $t=\frac{a}{b+c}$ holds, then $\alpha \le \beta$ and $\alpha \le \gamma$ . Note: The correctness of the answer must be proven.