min network in equiangular hexagon (V Soros Olympiad 1998-99 Round 1 10.9)
Source:
May 25, 2024
geometrygeometric inequalityhexagon
Problem Statement
Six cities are located at the vertices of a convex hexagon, all angles of which are equal. Three sides of this hexagon have length , and the remaining three have length (). It is necessary to connect these cities with a network of roads so that from each city you can drive to any other (possibly through other cities). Find the shortest length of such a road network.