\section*{Problem 1}

In the triangle \(\mathrm{ABC}\), the length of the altitude from \(\mathrm{A}\) is not less than \(\mathrm{BC}\), and the length of the altitude from \(\mathrm{B}\) is not less than \(\mathrm{AC}\). Find the angles.


\section*{Solution}

Let \(\mathrm{k}\) be twice the area of the triangle. Then \(\mathrm{k} \geq \mathrm{BC}^{2}, \mathrm{k} \geq \mathrm{AC}^{2}\) and \(\mathrm{k} \leq \mathrm{AC}\). \(\mathrm{BC}\), with equality in the last case only if \(\mathrm{AC}\) is perpendicular to \(\mathrm{BC}\). Hence \(\mathrm{AC}\) and \(\mathrm{BC}\) have equal lengths and are perpendicular. So the angles are \(90,45,45\).

