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Evaluation of the value of equal segments

Source: Bangladesh Mathematical Olympiad 2020 Problem 5

February 19, 2022
geometry

Problem Statement

In triangle ABCABC, AB=52AB = 52, BC=34BC = 34 and CA=50CA = 50. We split BCBC into nn equal segments by placing nāˆ’1n-1 new points. Among these points are the feet of the altitude, median and angle bisector from AA. What is the smallest possible value of nn?
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