MathDB

11.7

Part of 2001 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

9/26/2024
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|.
geometrycombinatoricscombinatorial geometrygeometric inequality