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Convex Polygon Diagonal Intersection Count

1800SpecialistCombinatoricsCounting Principles

Olimpiadas Matemáticas Españolas

Consider a convex polygon with $n$ sides. Draw all its diagonals and assume that no three of them meet at a point that is not a vertex, and that no two diagonals are parallel. Under these conditions, we wish to compute: a) The total number of intersection points of these diagonals, excluding the vertices. b) How many of these points are interior to the polygon, and how many are exterior.
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