MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 2
2023 Taiwan TST Round 2
3
3
Part of
2023 Taiwan TST Round 2
Problems
(1)
A delicious geometry in Taiwan TST
Source: 2023 Taiwan TST Round 2 Mock P3
4/7/2023
Let
Ω
\Omega
Ω
be the circumcircle of an acute triangle
A
B
C
ABC
A
BC
. Points
D
D
D
,
E
E
E
,
F
F
F
are the midpoints of the inferior arcs
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
, respectively, on
Ω
\Omega
Ω
. Let
G
G
G
be the antipode of
D
D
D
in
Ω
\Omega
Ω
. Let
X
X
X
be the intersection of lines
G
E
GE
GE
and
A
B
AB
A
B
, while
Y
Y
Y
the intersection of lines
F
G
FG
FG
and
C
A
CA
C
A
. Let the circumcenters of triangles
B
E
X
BEX
BEX
and
C
F
Y
CFY
CF
Y
be points
S
S
S
and
T
T
T
, respectively. Prove that
D
D
D
,
S
S
S
,
T
T
T
are collinear. Proposed by kyou46 and Li4.
geometry