MathDB
1997 MMO Grade 10 #3

Source:

October 3, 2016
Grade 101997

Problem Statement

A quadrilateral is rotated clockwise, and the sides are extended its length in the direction of the movement. It turns out the endpoints of the segments constructed form a square. Prove the initial quadrilateral must also be a square.
Generalization: Prove that if the same process is applied to any nn-gon and the result is a regular nn-gon, then the intial nn-gon must also be regular.