Consider the unit circle C: $\displaystyle x^2+y^2 = 1 $. Suppose 2 points are chosen randomly: (i) $\displaystyle p $ is chosen from the circumference and (ii) $\displaystyle q $ is chosen from the interior (chosen independently). Let $\displaystyle R $ be the rectangle with diagonal $\displaystyle pq $. What is the probability that no point of R lies outside of C?

Wouldn't a rectangle with diagonal $\displaystyle pq $ always lie inside the circle?