Let $G$ be a finitely generated hyperbolic group. Show that $G$ contains only finitely many conjugacy classes of elements of finite order.
In “Geometric Group Theory: An Introduction” by Clara Löh, it states in Exercise 7.E.19 that this can be proven from the fact that $G$ has a Dehn presentation by getting a bound on the minimal word length representing a finite order element. I understand there are stronger statements and other ways to prove this fact, but I can’t seem to see how to prove it directly using the fact that $G$ has a Dehn presentation.