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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
8.4
8.4
Part of
VI Soros Olympiad 1999 - 2000 (Russia)
Problems
(1)
TH bisects BC (VI Soros Olympiad 1990-00 R1 8.4)
Source:
5/27/2024
Let
C
H
CH
C
H
be the altitude of triangle ABC,
O
O
O
be the center of the circle circumscribed around it. Point
T
T
T
is the projection of point
C
C
C
on the line
T
O
TO
TO
. Prove that the line
T
H
TH
T
H
bisects the side
B
C
BC
BC
.
geometry
bisects segment