# rectangle

• Nov 24th 2009, 03:33 PM
Sampras
rectangle
Consider the unit circle C: $x^2+y^2 = 1$. Suppose 2 points are chosen randomly: (i) $p$ is chosen from the circumference and (ii) $q$ is chosen from the interior (chosen independently). Let $R$ be the rectangle with diagonal $pq$. What is the probability that no point of R lies outside of C?

Wouldn't a rectangle with diagonal $pq$ always lie inside the circle?
• Nov 24th 2009, 05:31 PM
TKHunny
The Diagonal pq will always be in or on the circle. Not so the other diagonal.

Easy demonstration:

$p = <0, 1>$

$q = <1-\epsilon , 0>$

Where $0 < \epsilon << 1$

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

Where is the North East vertex?