TxO Math Bowl 2024 - Team Contest - Problem 5

Consider a circle with radius 2 and center O. The center of a second circle P with radius 1 is picked inside the first circle at random. Given that the two circles intersect at 2 points, the probability that the distance between the two points of intersection is more than 1 can be expressed as \frac{\sqrt{a}-b}{c}, where a, b, and c are positive integers with b and c relatively prime. Find a + b + c.