Question 15
A rabbit is at some point $(x, y)$ in the Euclidean plane. There are some (possibly infinitely many) landmines, which are circles with any radius that do not intersect except possibly at one point (tangent). Every move, the rabbit can hop a distance of exactly $1$, but cannot land in the interior of a landmine (but may possibly land on the edge). Suppose that neither the rabbit nor the origin is in a landmine. Find the minimum $\varepsilon$ so that the rabbit can always reach a point with a distance of at most $\varepsilon$ from the origin, regardless of the landmine configuration.