White Circle in a Chessboard

Geometry Level 5

Consider an infinite chessboard, where the squares have side length of 1. The squares are colored black and white alternately. The (finite) radius of the largest circle whose circumference can be drawn completely on the white squares (hence you can see the entire circle) has the form \( \frac {a\sqrt{b}} {c} \), where \(a, b\) and \(c\) are integers, \(a\) and \(c\) are coprime, and \(b\) is not divisible by the square of any prime. What is the value of \(a + b + c\)?

Details and assumptions

\(a, b\) and \(c\) are all allowed to be 1. In particular, if you think the the largest radius is \( 1 = \frac {1 \sqrt{1}} {1} \), then your answer to this should be \(1+1+1=3\).

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