Question 8
Three circles, each of diameter $1$, are drawn each tangential to the others. A square enclosing the three circles is drawn so that two adjacent sides of the square are tangents to one of the circles and the square is as small as possible. The side length of this square is $a+\frac{\sqrt b+\sqrt c}{12}$ where $a,b,c$ are integers that are unique (except for swapping $b$ and $c$). Find $a+b+c$.