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Max-min of lengths in triangle

Source: Czech and Slovak Olympiad 1974, National Round, Problem 2

July 19, 2024
geometryTriangleminmax

Problem Statement

Let a triangle ABCABC be given. For any point XX of the triangle denote m(X)=min⁡{XA,XB,XC}.m(X)=\min\{XA,XB,XC\}. Find all points XX (of triangle ABCABC) such that m(X)m(X) is maximal.
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