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MMO 240 Moscow MO 1953 skew segments comparison

Source:

August 9, 2019
skewmidpointsgeometric inequalitygeometry3D geometry

Problem Statement

Let ABAB and A1B1A_1B_1 be two skew segments, OO and O1O_1 their respective midpoints. Prove that OO1OO_1 is shorter than a half sum of AA1AA_1 and BB1BB_1.
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