ProbabilityGeometry
A rectangle has width 2 and height 1.
Two points are chosen uniformly and independently from the interior of the rectangle:
- C, which becomes the centre of a circle, and
- P, which is a point on that circle.
So the circle is centred at C and has radius |CP|.
(0,1) +---------------------------------------+ (2,1)
| |
| .-~~~-. |
| / \ |
| | C | |
| \ * P |
| '-___-' |
| |
(0,0) +---------------------------------------+ (2,0)Question. What is the probability that the whole circle lies inside the rectangle (no part of it off the rectangle)? Give the exact value.