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Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
1
1
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Sharygin 2022 - P1
Source: Sharygin 2022 - P1 (Grade-8)
3/4/2022
Let
O
O
O
and
H
H
H
be the circumcenter and the orthocenter respectively of triangle
A
B
C
ABC
A
BC
. Itis known that
B
H
BH
B
H
is the bisector of angle
A
B
O
ABO
A
BO
. The line passing through
O
O
O
and parallel to
A
B
AB
A
B
meets
A
C
AC
A
C
at
K
K
K
. Prove that
A
H
=
A
K
AH = AK
A
H
=
A
K
geometry