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 -gon and the result is a regular -gon, then the intial -gon must also be regular.