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Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 1
2024 Taiwan TST Round 1
G
G
Part of
2024 Taiwan TST Round 1
Problems
(1)
Geometry in Taiwan TST
Source: 2024 Taiwan TST Round 1 Independent Study 2-G
3/7/2024
For the quadrilateral
A
B
C
D
ABCD
A
BC
D
, let
A
C
AC
A
C
and
B
D
BD
B
D
intersect at
E
E
E
,
A
B
AB
A
B
and
C
D
CD
C
D
intersect at
F
F
F
, and
A
D
AD
A
D
and
B
C
BC
BC
intersect at
G
G
G
. Additionally, let
W
,
X
,
Y
W, X, Y
W
,
X
,
Y
, and
Z
Z
Z
be the points of symmetry to
E
E
E
with respect to
A
B
,
B
C
,
C
D
,
AB, BC, CD,
A
B
,
BC
,
C
D
,
and
D
A
DA
D
A
respectively. Prove that one of the intersection points of
⊙
(
F
W
Y
)
\odot(FWY)
⊙
(
F
WY
)
and
⊙
(
G
X
Z
)
\odot(GXZ)
⊙
(
GXZ
)
lies on the line
F
G
FG
FG
.Proposed by chengbilly
geometry