2017 AIME I Problem 8

Two real numbers a and b are chosen independently and uniformly at random from the interval (0, 75). Let O and P be two points on the plane with OP = 200. Let Q and R be on the same side of line OP such that the degree measures of \angle POQ and \angle POR are a and b respectively, and \angle OQP and \angle ORP are both right angles. The probability that QR \leq 100 is equal to \frac{m}{n}, where m and n are relatively prime positive integers. Find m + n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.