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min of \sum PA_i, when A_i are collinear

Source: 1990 Swedish Mathematical Competition p2

April 2, 2021
SumGeometric Inequalitiesgeometrycollinear

Problem Statement

The points A1,A2,..,A2nA_1, A_2,.. , A_{2n} are equally spaced in that order along a straight line with A1A2=kA_1A_2 = k. PP is chosen to minimise ∑PAi\sum PA_i. Find the minimum.
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