Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main result focus on the event in which the intersection locates inside the fixed disc and establishes a sine law.
"Angle distribution of two random chords in the disc: A sine law." Braz. J. Probab. Stat. 35 (2) 263 - 280, May 2021. https://doi.org/10.1214/20-BJPS479