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Geometry with a lot of orthogonality

Source: European Mathematical Cup 2017 Junior,P3

December 28, 2017

geometry

Problem Statement

Let

ABC

be an acute triangle. Denote by

H

and

M

the orthocenter of

ABC

and the midpoint of side

BC,

respectively. Let

Y

be a point on

AC

such that

YH

is perpendicular to

MH

and let

Q

be a point on

BH

such that

QA

is perpendicular to

AM.

Let

J

be the second point of intersection of

MQ

and the circle with diameter

MY.

Prove that

HJ

is perpendicular to

AM.

(Steve Dinh)

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