Rectangle and Squares Inside a Circle

A rectangle with side lengths 6 and 8 is inscribed in a circle. Two congruent smaller squares are inscribed such that the two squares share a side, each square has one of its sides on the longer side of the rectangle, and each square has a vertex on the circle. What is the side length of either square? The answer is in the form $\frac{-a+\sqrt{b}}{c}$ where $a$, $b$, $c$ are positive integers, and $\gcd(a,c) = 1$. Input the value of $a+b+c$.