Problem #367
Circular Dilemma
Consider a rectangle with dimensions l = 1234567891 and b = 1987654321. A point is selected uniformly at random within the rectangle. From this point, a circle is drawn with a radius chosen uniformly between 0 and the maximum possible radius that allows the circle to remain entirely within the rectangle. What is the expected value of the \frac{\text{area of circle}}{π} \mod 10^9 + 7?