rectangle

Consider the unit circle C: . Suppose 2 points are chosen randomly: (i) is chosen from the circumference and (ii) is chosen from the interior (chosen independently). Let be the rectangle with diagonal . What is the probability that no point of R lies outside of C?

Wouldn't a rectangle with diagonal always lie inside the circle?

The Diagonal pq will always be in or on the circle. Not so the other diagonal.

Easy demonstration:





Where

p is the North West Vertex
q is the South East Vertex

Where is the North East vertex?