MathDB

6

Part of 1993 Miklós Schweitzer

Problems(1)

geometry

Source: miklos schweitzer 1993 q6

10/22/2021
Let P1,P2,...P_1 , P_2 , ... be arbitrary points and A be a connected compact set in the plane with a diameter greater than 4. Show that for some point P in A , PP1‾⋅PP2‾⋯PPn‾>1\overline {PP_1} \cdot \overline {PP_2} \cdots \overline {PP_n}>1. Furthermore, prove that this is no longer necessarily true for compact sets of diameter 4.
geometryinequalities