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geometry

Source: miklos schweitzer 1993 q6

October 22, 2021
geometryinequalities

Problem Statement

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.
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