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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?

Contributed by SANATAN SHARMA

Solved by 11 users

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