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ASU 073 All Russian MO 1966 |PA|+|PD|>|PB|+|PC|

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June 19, 2019
inequalitiesgeometric inequalitygeometry

Problem Statement

a) Points BB and CC are inside the segment [AD][AD]. ∣AB∣=∣CD∣|AB|=|CD|. Prove that for all of the points P on the plane holds inequality ∣PA∣+∣PD∣>∣PB∣+∣PC∣|PA|+|PD|>|PB|+|PC|
b) Given four points A,B,C,DA,B,C,D on the plane. For all of the points PP on the plane holds inequality ∣PA∣+∣PD∣>∣PB∣+∣PC∣.|PA|+|PD| > |PB|+|PC|. Prove that points BB and C are inside the segment [AD][AD] and∣AB∣=∣CD∣ |AB|=|CD|.
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