Difference

Since the triangle is inscribed in the circle then it's hypotenuse is also the diameter of the cricle so $y=10$ .

From the pythagorean theorem we can calculate that $y=x\sqrt { 5 }$ so $x=2\sqrt { 5 }$ .

The area of the blue shaded area is ${ x }^{ 2 }=20$ and the area of the orange shaded area is ${ 10 }^{ 2 }-\pi { 5 }^{ 2 }=100-25\pi$ .

The difference between them is $80-25\pi =5\left( 16-5\pi \right)$ . Therefore $a=5$ and $b=16$ and the digit sum of $b$ is $7$ ,

Finally $\overline { Baa } =755$ so the remainder is equal to $6$ .