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rioplatense perpendicularity

Source: Rioplatense Olympiad 2016 level 3 P3

September 4, 2018

geometryperpendicularmidpointsCircumcenterorthocenter

Problem Statement

Let

A B C

be an acute-angled triangle of circumcenter

O

and orthocenter

H

. Let

M

be the midpoint of

BC, N

be the symmetric of

H

with respect to

A, P

be the midpoint of

NM

and

X

be a point on the line A H such that

MX

is parallel to

CH

. Prove that

BX

and

OP

are perpendicular.