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Inequality in a triangle

Source: Czech and Slovak Olympiad 1983, National Round, Problem 2

April 10, 2020
geometric inequalitygeometryInequalitynational olympiadinequalities

Problem Statement

Given a triangle ABCABC, prove that for every inner point PP of the side ABAB the inequality PC⋅AB<PA⋅BC+PB⋅ACPC\cdot AB<PA\cdot BC+PB\cdot AC holds.
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