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2019-IMOC
G5
G5
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Problems
(1)
IMOC 2019 G5 (DH bisects <EDF, circumcircle, orthocenter related)
Source: https://artofproblemsolving.com/community/c6h1958463p13536764
3/22/2020
Given a scalene triangle
△
A
B
C
\vartriangle ABC
△
A
BC
with orthocenter
H
H
H
and circumcenter
O
O
O
. The exterior angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
intersects circumcircle of
△
A
B
C
\vartriangle ABC
△
A
BC
at
N
≠
A
N \ne A
N
=
A
. Let
D
D
D
be another intersection of
H
N
HN
H
N
and the circumcircle of
△
A
B
C
\vartriangle ABC
△
A
BC
. The line passing through
O
O
O
, which is parallel to
A
N
AN
A
N
, intersects
A
B
,
A
C
AB,AC
A
B
,
A
C
at
E
,
F
E, F
E
,
F
, respectively. Prove that
D
H
DH
DH
bisects the angle
∠
E
D
F
\angle EDF
∠
E
D
F
. https://3.bp.blogspot.com/-F1mFwojG_I0/XnYNR8ofqSI/AAAAAAAALeo/zge24WF0EO8umPAaXprKAeXJHAj7pr6tQCK4BGAYYCw/s1600/imoc2019g5.png
geometry
circumcircle