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Serbia National Math Olympiad
2023 Serbia National Math Olympiad
1
1
Part of
2023 Serbia National Math Olympiad
Problems
(1)
Geo involving centers of (AOH), (BOH), (COH)
Source: Serbia MO 2023 P1
4/2/2023
Given is a triangle
A
B
C
ABC
A
BC
with circumcenter
O
O
O
and orthocenter
H
H
H
. If
O
a
,
O
b
,
O
c
O_a, O_b, O_c
O
a
,
O
b
,
O
c
denote the circumcenters of
△
A
O
H
\triangle AOH
△
A
O
H
,
△
B
O
H
\triangle BOH
△
BO
H
,
△
C
O
H
\triangle COH
△
CO
H
, then prove that
A
O
a
,
B
O
b
,
C
O
c
AO_a, BO_b, CO_c
A
O
a
,
B
O
b
,
C
O
c
are concurrent.
geometry