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.
Problem
Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E14
Tags: combinatorics, geometry, combinatorial geometry