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Turkey MO (2nd round)
2022 Turkey MO (2nd round)
5
5
Part of
2022 Turkey MO (2nd round)
Problems
(1)
Circumcenter of $AHO$ and Euler Line
Source: Turkey National Mathematical Olympiad 2022 P5
12/23/2022
In triangle
A
B
C
ABC
A
BC
,
9
0
o
>
∠
A
>
∠
B
>
∠
C
90^{o}> \angle A> \angle B> \angle C
9
0
o
>
∠
A
>
∠
B
>
∠
C
. Let the circumcenter and orthocenter of the triangle be
O
O
O
and
H
H
H
.
O
H
OH
O
H
intersects
B
C
BC
BC
at
T
T
T
and the circumcenter of
(
A
H
O
)
(AHO)
(
A
H
O
)
is
X
X
X
. Prove that the reflection of
H
H
H
over
X
T
XT
XT
lies on the circumcircle of triangle
A
B
C
ABC
A
BC
.
geometry