# You take one side, I'll take the other

Calculus Level 4

Suppose we have two concentric circles of radii $$3$$ and $$4$$, respectively. Let $$R$$ be the largest rectangle with two adjacent vertices on the radius $$3$$ circle and two adjacent vertices on the radius $$4$$ circle.

Let $$x$$ and $$y$$ be the dimensions of $$R$$, with $$x \gt y$$. Then if $$x - y = \dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, find $$a + b$$.

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