I'm trying to study Hyperbolic geometry, but I can not understand the following statement.
Let $X$ be a $δ$-hyperbolic space. Then, there exists $M > 0$ such that for any geodesic $γ$, and any ball $B_r(x)$ of arbitrary radius that is disjoint from $γ$, the closest-point projection of the ball to the geodesic has diameter $≤ M$.
I want to know the proof of the question. (Maybe $M = 5δ$)
If anyone could help, It would be really appreciated.Thanks.