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5
2013 HMMT Geometry # 5
2013 HMMT Geometry # 5
Source:
March 3, 2024
geometry
Problem Statement
In triangle
A
B
C
ABC
A
BC
,
∠
A
=
4
5
o
\angle A = 45^o
∠
A
=
4
5
o
and
M
M
M
is the midpoint of
B
C
‾
\overline{BC}
BC
.
A
M
‾
\overline{AM}
A
M
intersects the circumcircle of
A
B
C
ABC
A
BC
for the second time at
D
D
D
, and
A
M
=
2
M
D
AM = 2MD
A
M
=
2
M
D
. Find
c
o
s
∠
A
O
D
cos\angle AOD
cos
∠
A
O
D
, where
O
O
O
is the circumcenter of
A
B
C
ABC
A
BC
.
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