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Nepal Contests
Nepal National Olympiad
2024 Nepal Mathematics Olympiad (Pre-TST)
Problem 3
Problem 3
Part of
2024 Nepal Mathematics Olympiad (Pre-TST)
Problems
(1)
NMO (Nepal) Problem 3
Source:
3/17/2024
Let
A
B
C
ABC
A
BC
be an acute triangle and
H
H
H
be its orthocenter. Let
E
E
E
be the foot of the altitude from
C
C
C
to
A
B
AB
A
B
,
F
F
F
be the foot of the altitude from
B
B
B
to
A
C
AC
A
C
. Let
G
≠
H
G \neq H
G
=
H
be the intersection of the circles
(
A
E
F
)
(AEF)
(
A
EF
)
and
(
B
H
C
)
(BHC)
(
B
H
C
)
. Prove that
A
G
AG
A
G
bisects
B
C
BC
BC
.Proposed by Kang Taeyoung, South Korea
geometry