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Source: Indian IMOTC 2005 Day 2 Problem 1

September 17, 2005
geometry solvedgeometry

Problem Statement

Consider a nn-sided polygon inscribed in a circle (n≥4n \geq 4). Partition the polygon into n−2n-2 triangles using non-intersecting diagnols. Prove that, irrespective of the triangulation, the sum of the in-radii of the triangles is a constant.
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