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6
2015 Geometry #6
2015 Geometry #6
Source:
December 23, 2016
Problem Statement
In triangle
A
B
C
ABC
A
BC
,
A
B
=
2
AB=2
A
B
=
2
,
A
C
=
1
+
5
AC=1+\sqrt{5}
A
C
=
1
+
5
, and
∠
C
A
B
=
5
4
∘
\angle CAB=54^{\circ}
∠
C
A
B
=
5
4
∘
. Suppose
D
D
D
lies on the extension of
A
C
AC
A
C
through
C
C
C
such that
C
D
=
5
−
1
CD=\sqrt{5}-1
C
D
=
5
−
1
. If
M
M
M
is the midpoint of
B
D
BD
B
D
, determine the measure of
∠
A
C
M
\angle ACM
∠
A
CM
, in degrees.
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