KöMaL 2026 B5553

In triangle $ABC$ let $a<b<c$, $m_a$, $m_b$, $m_c$ and $r_a$, $r_b$, $r_c$ be the sides, the heights and the exradii (using the usual notations). Find all possible orders by magnitude of $m_a$, $m_b$, $m_c$, $r_a$, $r_b$, $r_c$.