Question 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 in the plane with $OP = 200.$ Let $Q$ and $R$ be points 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 $QR \le 100$ is equal to $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$