MathDB

A square has coordinates at

(0, 0)

(4, 0)

(0, 4)

, and

(4, 4)

. Rohith is interested in circles of radius

r

centered at the point

(1, 2)

. There is a range of radii

a < r < b

where Rohith’s circle intersects the square at exactly

6

points, where

a

and

b

are positive real numbers. Then

b - a

can be written in the form

m +\sqrt{n}

, where

m

and

n

are integers. Compute

m + n

Problem Statement