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India Contests
India EGMO TST
India EGMO 2024 TST
6
6
Part of
India EGMO 2024 TST
Problems
(1)
Interesting conditional geo in orthocentre configuration
Source: India EGMO TST 2024/6
12/31/2023
Let
A
B
C
ABC
A
BC
be an acute angled triangle with orthocentre
H
H
H
. Let
E
=
B
H
∩
A
C
E = BH \cap AC
E
=
B
H
∩
A
C
and
F
=
C
H
∩
A
B
F= CH \cap AB
F
=
C
H
∩
A
B
. Let
D
,
M
,
N
D, M, N
D
,
M
,
N
denote the midpoints of segments
A
H
,
B
D
,
C
D
AH, BD, CD
A
H
,
B
D
,
C
D
respectively, and
T
=
F
M
∩
E
N
T = FM \cap EN
T
=
FM
∩
EN
. Suppose
D
,
E
,
T
,
F
D, E, T, F
D
,
E
,
T
,
F
are concylic. Prove that
D
T
DT
D
T
passes through the circumcentre of
A
B
C
ABC
A
BC
.Proposed by Pranjal Srivastava
geometry
Egmo tst