Problem

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E14

Tags: combinatorics, geometry, combinatorial geometry



Zeus’s lightning is made of a copper rod of length $60$ by bending it $4$ times in alternating directions so that the angle between two adjacent parts is always $60^o$. What is the minimum value of the square of the distance between the two endpoints of the lightning? All five segments of the lightning lie in the same plane.