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International Contests
Czech-Polish-Slovak Match
2023 Czech-Polish-Slovak Match
5
5
Part of
2023 Czech-Polish-Slovak Match
Problems
(1)
Orthocenter geo
Source: CAPS Match 2023 P5
6/30/2023
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with orthocenter
H
H
H
. Let
D
D
D
be the foot of the altitude from
A
A
A
to the line
B
C
BC
BC
. Let
T
T
T
be a point on the circle with diameter
A
H
AH
A
H
such that this circle is internally tangent to the circumcircle of triangle
B
D
T
BDT
B
D
T
. Let
N
N
N
be the midpoint of segment
A
H
AH
A
H
. Prove that
B
T
⊥
C
N
BT \perp CN
BT
⊥
CN
.
geometry