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1of DA, DB, DC exceeds 1 of PA, PB and PC, tetrahedron ABCD

Source: 1962 Hungary - Kürschák Competition p3

October 11, 2022
geometry3D geometrytetrahedronGeometric Inequalities

Problem Statement

PP is any point of the tetrahedron ABCDABCD except DD. Show that at least one of the three distances DADA, DBDB, DCDC exceeds at least one of the distances PAPA, PBPB and PCPC.
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