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National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2021 Moldova EGMO TST
7
7
Part of
2021 Moldova EGMO TST
Problems
(1)
Prove that the lines $AM, BN, CP$ and $OH$ are concurrent.
Source: Moldova EGMO TST 2021
2/4/2023
A triangle
A
B
C
ABC
A
BC
has the orthocenter
H
H
H
different from the vertexes and the circumcenter
O
O
O
. Let
M
,
N
M, N
M
,
N
and
P
P
P
be the circumcenters of triangles
H
B
C
,
H
C
A
HBC, HCA
H
BC
,
H
C
A
and
H
A
B
HAB
H
A
B
. Prove that the lines
A
M
,
B
N
,
C
P
AM, BN, CP
A
M
,
BN
,
CP
and
O
H
OH
O
H
are concurrent.
geometry
circumcircle