Chord Through a Random Point
A point P is chosen uniformly at random inside a disk of radius 1. Then a line through P is drawn in a direction chosen uniformly at random, independent of P. The line meets the disk in a chord. What is the probability that this chord is longer than √3 (the side of the inscribed equilateral triangle)? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- Break the Longer Piece 6.0/10
- Real Roots at Random 6.0/10
- The Midpoint Chord 6.0/10
Source: Original problem written for AxiomIQ.