Obtuse in a Square
Three points are chosen independently and uniformly at random in the unit square. What is the probability that the triangle they form is obtuse? 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: Result due to Eric Langford, 'The probability that a random triangle is obtuse', Biometrika (1969). Statement written for AxiomIQ.