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2018-IMOC
G5
G5
Part of
2018-IMOC
Problems
(1)
IMOC 2018 G5 (IX//OH, incenter, circumcenter, orthocenter, euler line)
Source: https://artofproblemsolving.com/community/c6h1740825p11314688
3/22/2020
Suppose
I
,
O
,
H
I,O,H
I
,
O
,
H
are incenter, circumcenter, orthocenter of
△
A
B
C
\vartriangle ABC
△
A
BC
respectively. Let
D
=
A
I
∩
B
C
D = AI \cap BC
D
=
A
I
∩
BC
,
E
=
B
I
∩
C
A
E = BI \cap CA
E
=
B
I
∩
C
A
,
F
=
C
I
∩
A
B
F = CI \cap AB
F
=
C
I
∩
A
B
and
X
X
X
be the orthocenter of
△
D
E
F
\vartriangle DEF
△
D
EF
. Prove that
I
X
∥
O
H
IX \parallel OH
I
X
∥
O
H
.
geometry
incenter
Circumcenter
orthocenter
parallel
Euler Line