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Nordic
2018 Nordic
3
3
Part of
2018 Nordic
Problems
(1)
Orthocenter of BCI lies on DE
Source: Nordic Mathematical Contest 2018 Problem 3
4/10/2018
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
<
A
C
AB < AC
A
B
<
A
C
. Let
D
D
D
and
E
E
E
be on the lines
C
A
CA
C
A
and
B
A
BA
B
A
, respectively, such that
C
D
=
A
B
CD = AB
C
D
=
A
B
,
B
E
=
A
C
BE = AC
BE
=
A
C
, and
A
A
A
,
D
D
D
and
E
E
E
lie on the same side of
B
C
BC
BC
. Let
I
I
I
be the incenter of triangle
A
B
C
ABC
A
BC
, and let
H
H
H
be the orthocenter of triangle
B
C
I
BCI
BC
I
. Show that
D
D
D
,
E
E
E
, and
H
H
H
are collinear.
geometry