MathDB
|XA|, |XB| >=0.999|AB| - All-Russian MO 2001 Regional (R4) 11.7

Source:

September 26, 2024
geometrycombinatoricscombinatorial geometrygeometric inequality

Problem Statement

There is an infinite set of points SS on the plane, and any 1×11\times 1 square contains a finite number of points from the set SS. Prove that there are two different points AA and BB from SS such that for any other point XX from SS the following inequalities hold: ∣XA∣,∣XB∣≥0.999∣AB∣.|XA|, |XB| \ge 0.999|AB|.
Back to ProblemsView on AoPS