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5
SMT 2018 Geometry #5
SMT 2018 Geometry #5
Source:
August 8, 2023
geometry
Problem Statement
In
△
A
B
C
\vartriangle ABC
△
A
BC
,
∠
A
B
C
=
7
5
o
\angle ABC = 75^o
∠
A
BC
=
7
5
o
and
∠
B
A
C
\angle BAC
∠
B
A
C
is obtuse. Points
D
D
D
and
E
E
E
are on
A
C
AC
A
C
and
B
C
BC
BC
, respectively, such that
A
B
B
C
=
D
E
E
C
\frac{AB}{BC} = \frac{DE}{EC}
BC
A
B
=
EC
D
E
and
∠
D
E
C
=
∠
E
D
C
\angle DEC = \angle EDC
∠
D
EC
=
∠
E
D
C
. Compute
∠
D
E
C
\angle DEC
∠
D
EC
in degrees.
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