Cutting Off a Segment
Two points are chosen independently and uniformly on the boundary of a disk, and the chord joining them cuts the disk into two pieces. What is the expected area of the smaller piece, as a fraction of the disk's area? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- All in a Semicircle 5.0/10
- An Obtuse Viewing Angle 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.