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Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2023 Iran MO (3rd Round)
6
6
Part of
2023 Iran MO (3rd Round)
Problems
(1)
Another triangle geo
Source: Iran MO 2023 3rd round , Day 2 P3
8/16/2023
In the acute triangle
△
A
B
C
\triangle ABC
△
A
BC
,
H
H
H
is the orthocenter.
S
S
S
is a point on
(
A
H
C
)
(AHC)
(
A
H
C
)
st
∠
A
S
B
=
90
\angle ASB = 90
∠
A
SB
=
90
.
P
P
P
is on
A
C
AC
A
C
and not on the extention of
A
C
AC
A
C
from
A
A
A
, st
∠
A
P
S
=
∠
B
A
S
\angle APS=\angle BAS
∠
A
PS
=
∠
B
A
S
.Prove that
C
S
CS
CS
, the circle
(
B
P
C
)
(BPC)
(
BPC
)
and the circle with diameter
A
C
AC
A
C
are concurrent.
geometry