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2023 Poland - Second Round
5
5
Part of
2023 Poland - Second Round
Problems
(1)
Cute Polish geo with weird orthocenter
Source: Polish MO 2nd round 2023/5
2/11/2023
Given is a triangle
A
B
C
ABC
A
BC
with
A
B
>
A
C
AB>AC
A
B
>
A
C
. Its incircle touches
A
B
,
A
C
AB, AC
A
B
,
A
C
at
D
,
E
D, E
D
,
E
, respectively. Let
C
D
CD
C
D
meet the incircle at
K
K
K
and
L
L
L
is the foot of the perpendicular from
A
A
A
to
C
K
CK
C
K
. If
M
M
M
is the midpoint of
D
E
DE
D
E
and
H
H
H
is the orthocenter of
△
K
M
L
\triangle KML
△
K
M
L
, prove that
∠
A
H
K
=
9
0
o
\angle AHK=90^{o}
∠
A
HK
=
9
0
o
.Proposed by Dominik Burek
geometry