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SAFEST (South Africa - Estonia) Olympiad
2020 SAFEST Olympiad
2020 SAFEST Olympiad
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<OAH = <LSA wanted, circumcenter, orthocenter, midpoint, perp. bisector
Let
O
O
O
be the circumcenter and
H
H
H
the orthocenter of an acute-triangle
A
B
C
ABC
A
BC
. The perpendicular bisector of
A
O
AO
A
O
intersects the line
B
C
BC
BC
at point
S
S
S
. Let
L
L
L
be the midpoint of
O
H
OH
O
H
. Prove that
∠
O
A
H
=
∠
L
S
A
\angle OAH = \angle LSA
∠
O
A
H
=
∠
L
S
A
.