The Midpoint Chord
A point M is chosen uniformly at random inside a disk of radius 1, and the chord of the disk whose midpoint is M is drawn. (If M is the centre, which happens with probability 0, any diameter will do.) What is the expected length of the chord? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- An Obtuse Viewing Angle 5.0/10
- Buffon's Needle 5.0/10
- Rounding a Ratio 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.