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Orthocenter condition

Source: CWMI 2017 Q6

August 14, 2017

geometry

Problem Statement

In acute triangle

ABC

, let

D

and

E

be points on sides

AB

and

AC

respectively. Let segments

BE

and

DC

meet at point

H

. Let

M

and

N

be the midpoints of segments

BD

and

CE

respectively. Show that

H

is the orthocenter of triangle

AMN

if and only if

B,C,E,D

are concyclic and

BE\perp CD

.

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