Problem of the Day #91

POTD March 9, 2024

A rectangle with height 2 and length 4\sqrt{3} is inscribed in a semicircle with the diameter touching the rectangle’s longer side by. Let x be the area of the the sector formed by the intersection of the rectangle and circle. If \frac{x}{\pi} = \frac{a}{b}, where a and b are relatively prime, positive integers, find a+b.