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Problems
Contests
National and Regional Contests
China Contests
China Team Selection Test
2024 China Team Selection Test
22
22
Part of
2024 China Team Selection Test
Problems
(1)
XEY is fixed
Source: 2024 CTST P22
3/29/2024
A
B
C
ABC
A
BC
is an isosceles triangle, with
A
B
=
A
C
AB=AC
A
B
=
A
C
.
D
D
D
is a moving point such that
A
D
∥
B
C
AD\parallel BC
A
D
∥
BC
,
B
D
>
C
D
BD>CD
B
D
>
C
D
. Moving point
E
E
E
is on the arc of
B
C
BC
BC
in circumcircle of
A
B
C
ABC
A
BC
not containing
A
A
A
, such that
E
B
<
E
C
EB<EC
EB
<
EC
. Ray
B
C
BC
BC
contains point
F
F
F
with
∠
A
D
E
=
∠
D
F
E
\angle ADE=\angle DFE
∠
A
D
E
=
∠
D
FE
. If ray
F
D
FD
F
D
intersects ray
B
A
BA
B
A
at
X
X
X
, and intersects ray
C
A
CA
C
A
at
Y
Y
Y
, prove that
∠
X
E
Y
\angle XEY
∠
XE
Y
is a fixed angle.
geometry
2024 CTST