all angles of a convex $n$-gon are equal
Source: All-Russian olympiad 1995, Grade 10, First Day, Problem 4
October 20, 2013
geometry proposedgeometry
Problem Statement
Prove that if all angles of a convex -gon are equal, then there are at least two of its sides that are not longer than their adjacent sides.
A. Berzin’sh, O. Musin