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China Team Selection Test
2024 China Team Selection Test
17
Geometry with two cases
Geometry with two cases
Source: 2024 CTST P17
March 25, 2024
geometry
Problem Statement
A
B
C
D
E
ABCDE
A
BC
D
E
is a convex pentagon with
B
D
=
C
D
=
A
C
BD=CD=AC
B
D
=
C
D
=
A
C
, and
B
B
B
,
C
C
C
,
D
D
D
,
E
E
E
are concyclic. If
∠
B
A
C
+
∠
A
E
D
=
18
0
∘
\angle BAC+\angle AED=180^{\circ}
∠
B
A
C
+
∠
A
E
D
=
18
0
∘
and
∠
D
C
A
=
∠
B
D
E
\angle DCA=\angle BDE
∠
D
C
A
=
∠
B
D
E
, prove that
A
B
=
D
E
AB=DE
A
B
=
D
E
or
A
B
=
2
A
E
AB=2AE
A
B
=
2
A
E
.
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