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EF//GH if < EAF = 45^o, given square ABCD and it's circumcircle

Source: Mathematics Regional Olympiad of Mexico West 2019 P2

September 9, 2022

parallelsquaregeometry

Problem Statement

Given a square

ABCD

, points

E

and

F

are taken inside the segments

BC

and

CD

so that

\angle EAF = 45^o

. The lines

AE

and

AF

intersect the circle circumscribed to the square at points

G

and

H

respectively. Prove that lines

EF

and

GH

are parallel.