Difference

Geometry Level 3

The diagram above shows a circle inscribed inside a square of side length 1010, which has a right triangle of legs length xx and 2x2x, and hypotenuse length yy inscribed in it.

The difference between the area of the orange\color{#ee7600}{\text{orange}} shaded region and the blue\color{#3D99F6}{\text{blue}} shaded region can be written as a(baπ)a(b-a\pi ) for integers aa and bb. Let the digit sum of bb be BB. Then find the remainder of Baa÷B\large\overline { Baa } \div B

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