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Prove that $AH$ and $CK$ are parallel.

Source: Moldova EGMO TST 2021

February 4, 2023

geometry

Problem Statement

Let

ABCD

be a square and

E

a on point diagonal

(AC)

, different from its midpoint.

H

and

K

are the orthoceneters of triangles

ABE

and

ADE

. Prove that

AH

and

CK

are parallel.

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