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21
2017 Guts #21
2017 Guts #21
Source:
November 25, 2022
2017
Guts Round
Problem Statement
In trapezoid
A
B
C
D
ABCD
A
BC
D
, we have
A
D
‾
∥
B
C
‾
\overline{AD}\parallel\overline{BC}
A
D
∥
BC
,
B
C
=
3
BC=3
BC
=
3
, and
C
D
=
4
CD=4
C
D
=
4
. In addition,
cos
∠
A
D
C
=
1
3
\cos\angle ADC=\tfrac{1}{3}
cos
∠
A
D
C
=
3
1
and
∠
A
B
C
=
2
∠
A
D
C
\angle ABC=2\angle ADC
∠
A
BC
=
2∠
A
D
C
. Compute
A
C
AC
A
C
.
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