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incenter of AIB, etc., limit of sequence

Source: VJIMC 2009 1.1

June 12, 2021
geometryincenterlimits

Problem Statement

Let ABCABC be a non-degenerate triangle in the euclidean plane. Define a sequence (Cn)n=0∞(C_n)_{n=0}^\infty of points as follows: C0:=CC_0:=C, and Cn+1C_{n+1} is the incenter of the triangle ABCnABC_n. Find lim⁡n→∞Cn\lim_{n\to\infty}C_n.
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