2018_Question1_e

2018_Question1_f

The answer is (a).

A circle of radius 2 has 13 points within (or on) the circle. Therefore 2n - 5 = 21.

The 8 extra points closest to the boundary of the circle are at (1,2),(-1,2),(2,1),(2,-1),(1,-2),(-1,-2),(-2,-1),(-2,1).

These points are all a distance of sqrt(5) from the origin. Therefore the radius must increase by sqrt(5) - 2.

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