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8
2015 Geometry #8
2015 Geometry #8
Source:
July 1, 2022
2015
Geometry Test
Problem Statement
In triangle
A
B
C
ABC
A
BC
, point
D
D
D
is on side
B
C
BC
BC
such that
A
D
AD
A
D
is the angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
. If
A
B
=
12
AB=12
A
B
=
12
,
A
D
=
9
AD=9
A
D
=
9
, and
A
C
=
15
AC=15
A
C
=
15
, compute
cos
∠
B
A
C
2
\cos\tfrac{\angle BAC}{2}
cos
2
∠
B
A
C
.
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