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Right angles and orthocentre

Source: Romania JBMO TST 2024 Day 2 P3

July 31, 2024

geometry

Problem Statement

In the exterior of the acute-angles triangle

ABC

we construct the isosceles triangles

DAB

and

EAC

with bases

AB{}

and

AC{}

respectively such that

\angle DBC=\angle ECB=90^\circ.

Let

M

and

N

be the reflections of

A

with respect to

D

and

E

respectively. Prove that the line

MN

passes through the orthocentre of the triangle

ABC.

Florin Bojor

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