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Four vertices of special equilateral 8-gon are concyclic

Source: IV Caucasus Mathematic Olympiad

April 7, 2019

geometry

Problem Statement

Points

A'

and

B'

lie inside the parallelogram

ABCD

and points

C'

and

D'

lie outside of it, so that all sides of 8-gon

AA'BB'CC'DD'

are equal. Prove that

A'

B'

C'

D'

are concyclic.