Problem

Source: China Mathematical Olympiad 1986 problem2

Tags: trigonometry, geometry, trig identities, Law of Sines, geometry unsolved



In $\triangle ABC$, the length of altitude $AD$ is $12$, and the bisector $AE$ of $\angle A$ is $13$. Denote by $m$ the length of median $AF$. Find the range of $m$ when $\angle A$ is acute, orthogonal and obtuse respectively.