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minimum number of bisector in a convex polygon

Source: Brazilian Mathematical Olympiad 2024, Level 3, Problem 3

October 12, 2024
geometrycombinatorial geometryangle bisectordiagonals

Problem Statement

Let n≥3 n \geq 3 be a positive integer. In a convex polygon with n n sides, all the internal bisectors of its n n internal angles are drawn. Determine, as a function of n n , the smallest possible number of distinct lines determined by these bisectors.
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