Difference

Geometry Level 3

The diagram above shows a circle inscribed inside a square of side length \(10\), which has a right triangle of legs length \(x\) and \(2x\), and hypotenuse length \(y\) inscribed in it.

The difference between the area of the \(\color{#ee7600}{\text{orange}}\) shaded region and the \(\color{blue}{\text{blue}}\) shaded region can be written as \(a(b-a\pi )\) for integers \(a\) and \(b\). Let the digit sum of \(b\) be \(B\). Then find the remainder of \[\large\overline { Baa } \div B \]

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