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Iran MO (2nd Round)
2023 Iran MO (2nd Round)
P1
P1
Part of
2023 Iran MO (2nd Round)
Problems
(1)
2023 Iran MO 2nd round P1
Source: 2023 Iran MO
5/17/2023
1. In right triangle
A
B
C
ABC
A
BC
with \angle{A}= \textdegree{90}, point
P
P
P
is chosen.
D
∈
B
C
D \in BC
D
∈
BC
such that
P
D
⊥
B
C
PD \perp BC
P
D
⊥
BC
. Let the intersection of
P
D
PD
P
D
with
A
B
AB
A
B
and
A
C
AC
A
C
be
E
E
E
and
F
F
F
respectively. Denote by
X
X
X
and
Y
Y
Y
as the intersection of
(
A
P
E
)
(APE)
(
A
PE
)
and
(
A
P
F
)
(APF)
(
A
PF
)
with
B
P
BP
BP
and
C
P
CP
CP
respectively. Prove that
C
X
,
B
Y
,
P
D
CX,BY,PD
CX
,
B
Y
,
P
D
are concurrent.
geometry