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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)

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    get some graph paper, also called quadrille paper, draw some pictures. This is not difficult. http://en.wikipedia.org/wiki/Graph_paper2012-02-07

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