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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2013.7
2013.7
Part of
Swiss NMO - geometry
Problems
(1)
ST bisects BC, <ASO = <ACO, <ATO =< ABO
Source: Switzerland - Swiss MO 2013 p7
7/16/2020
Let
O
O
O
be the center of the circle of the triangle
A
B
C
ABC
A
BC
with
A
B
≠
A
C
AB \ne AC
A
B
=
A
C
. Furthermore, let
S
S
S
and
T
T
T
be points on the rays
A
B
AB
A
B
and
A
C
AC
A
C
, such that
∠
A
S
O
=
∠
A
C
O
\angle ASO = \angle ACO
∠
A
SO
=
∠
A
CO
and
∠
A
T
O
=
∠
A
B
O
\angle ATO = \angle ABO
∠
A
TO
=
∠
A
BO
. Show that
S
T
ST
ST
bisects the segment
B
C
BC
BC
.
geometry
bisects segment
equal angles