MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2021-IMOC qualification
G3
G3
Part of
2021-IMOC qualification
Problems
(1)
Triangle with 45 degree angle and the Nine Point Center
Source: 2021 IMOC qualification problem, G3
12/30/2021
Given a
△
A
B
C
\triangle ABC
△
A
BC
,
∠
A
=
4
5
∘
\angle A=45^\circ
∠
A
=
4
5
∘
,
O
O
O
is the circumcenter and
H
H
H
is the orthocenter of
△
A
B
C
\triangle ABC
△
A
BC
.
M
M
M
is the midpoint of
B
C
‾
\overline{BC}
BC
, and
N
N
N
is the midpoint of
O
H
‾
\overline{OH}
O
H
. Prove that
∠
B
A
M
=
∠
C
A
N
\angle BAM=\angle CAN
∠
B
A
M
=
∠
C
A
N
.
IMOC
geometry