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DHMO is a parallelogram

Source: MEMO 2018 T5

September 3, 2018

geometryparallelogramOHM

Problem Statement

Let

ABC

be an acute-angled triangle with

AB<AC,

and let

D

be the foot of its altitude from

A,

points

B'

and

C'

lie on the rays

AB

and

AC,

respectively , so that points

B',

C'

and

D

are collinear and points

B,

C,

B'

and

C'

lie on one circle with center

O.

Prove that if

M

is the midpoint of

BC

and

H

is the orthocenter of

ABC,

then

DHMO

is a parallelogram.

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