Let us get a little poetic here: "A rose between two thorns... A circle between two squares..."

In the figure, we see a circle resting between two squares which touch it from either side. The circle is tangential to the line joining the bottoms of the squares. The left square has side length 2 and the right square has side length 1. The distance separating the two squares is 6.

If the radius of the circle can be expressed as \(\frac{a}{b} -c\sqrt{d},\) where \(a\) and \(b\) are coprime positive integers and \(d\) is the smallest possible positive integer, then find \(a + b + c + d\).

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