MathDB

Geometry with circle, square and parallel lines

Source: Bundeswettbewerb Mathematik 2019, Round 1 - Problem 3

August 5, 2019

geometrycircumcirclesquare

Problem Statement

Let

ABCD

be a square. Choose points

E

BC

and

F

CD

so that

\angle EAF=45^\circ

and so that neither

E

nor

F

is a vertex of the square. The lines

AE

and

AF

intersect the circumcircle of the square in the points

G

and

H

distinct from

A

, respectively. Show that the lines

EF

and

GH

are parallel.