Suppose that circles with radius r are drawn with lattice points as centres. Find the smallest value of r such that any line of form y =$\frac{2}{5}x$+c intersects some of these circles.
The way I was thinking of approaching this was to find the c that gives the maximum distance from the lattice points, then calculate the needed r- but I wasn't able to get that to work.
(This is #23 Problems Plus Chapter 3 Calculus Early Transcendentals)