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Cono Sur Olympiad
2003 Cono Sur Olympiad
3
3
Part of
2003 Cono Sur Olympiad
Problems
(1)
Acute triangle and semicircle with diameter AC
Source: Cono Sur 2003 #3
11/18/2015
Let
A
B
C
ABC
A
BC
be an acute triangle such that
∠
B
=
60
\angle{B}=60
∠
B
=
60
. The circle with diameter
A
C
AC
A
C
intersects the internal angle bisectors of
A
A
A
and
C
C
C
at the points
M
M
M
and
N
N
N
, respectively
(
M
≠
A
,
(M\neq{A},
(
M
=
A
,
N
≠
C
)
N\neq{C})
N
=
C
)
. The internal bisector of
∠
B
\angle{B}
∠
B
intersects
M
N
MN
MN
and
A
C
AC
A
C
at the points
R
R
R
and
S
S
S
, respectively. Prove that
B
R
≤
R
S
BR\leq{RS}
BR
≤
RS
.
geometry
cono sur