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2017 USAJMO
5
5
Part of
2017 USAJMO
Problems
(1)
Show that angle ADO = angle HAN
Source: JMO 2017 P5
4/20/2017
Let
O
O
O
and
H
H
H
be the circumcenter and the orthocenter of an acute triangle
A
B
C
ABC
A
BC
. Points
M
M
M
and
D
D
D
lie on side
B
C
BC
BC
such that
B
M
=
C
M
BM=CM
BM
=
CM
and
∠
B
A
D
=
∠
C
A
D
\angle BAD = \angle CAD
∠
B
A
D
=
∠
C
A
D
. Ray
M
O
MO
MO
intersects the circumcircle of triangle
B
H
C
BHC
B
H
C
in point
N
N
N
. Prove that
∠
A
D
O
=
∠
H
A
N
\angle ADO = \angle HAN
∠
A
D
O
=
∠
H
A
N
.
USAJMO
geometry