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Contests
National and Regional Contests
China Contests
China Team Selection Test
2024 China Team Selection Test
17
17
Part of
2024 China Team Selection Test
Problems
(1)
Geometry with two cases
Source: 2024 CTST P17
3/25/2024
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
.
geometry