\(\color{blue}{This}\) \(\color{blue}{is}\) \(\color{blue}{a}\) \(\color{blue}{2015}\) \(\color{blue}{AMC}\) \(\color{blue}{12}\) \(\color{blue}{problem.}\)

A square with side length 1 inches is drawn. If 2 points are to be picked randomly from the perimeter of the square (can be anywhere on the perimeter), what is your probability that the distance between the two points will be greater the 0.5 inches? Your answer can be expressed as \(\huge \frac{a + b\pi}{c}\), where the fraction is in simplest form., and all variables are integers, and \(a\) and \(c\) are natural numbers.

Find \(a^{2}\) + \(b\) - \(2c\)

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