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4 cities - All-Russian MO 1994 Regional (R4) 9.2

Source:

August 26, 2024
combinatorics

Problem Statement

Cities A,B,C,DA,B,C,D are positioned in such a way that AA is closer to CC than to DD, and BB is closer to CC than to DD. Prove that every point on the straight road from AA to BB is closer to CC than to DD.
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