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perpendicular wanted, orthocenter related

Source: Switzerland - Swiss MO 2007 p4

July 18, 2020

geometryperpendicularorthocenter

Problem Statement

Let

ABC

be an acute-angled triangle with

AB> AC

and orthocenter

H

. Let

D

the projection of

A

on

BC

. Let

E

be the reflection of

C

wrt

D

. The lines

MN

and

BH

intersect at point

S

. Let

N

be the midpoint of

AE

and let

M

be the midpoint of

BH

. Prove that

MN

is perpendicular to

DS

.

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