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Intersections of random chords of a circle
Cynthia Bortolotto, Victor Souza · 2025-04-17 · via math.PR updates on arXiv.org

Where are the intersection points of diagonals of a regular $n$-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability, extend a largely forgotten result of Karamata, and elucidate its connection to the Bertrand paradox.

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