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Bulgaria National Olympiad
2021 Bulgaria National Olympiad
2
2
Part of
2021 Bulgaria National Olympiad
Problems
(1)
point on the altitude
Source: Bulgaria NMO 2021P2
5/16/2021
A point
T
T
T
is given on the altitude through point
C
C
C
in the acute triangle
A
B
C
ABC
A
BC
with circumcenter
O
O
O
, such that
∡
T
B
A
=
∡
A
C
B
\measuredangle TBA=\measuredangle ACB
∡
TB
A
=
∡
A
CB
. If the line
C
O
CO
CO
intersects side
A
B
AB
A
B
at point
K
K
K
, prove that the perpendicular bisector of
A
B
AB
A
B
, the altitude through
A
A
A
and the segment
K
T
KT
K
T
are concurrent.
geometry